...4. A number is divisible by 5. If the last digit is either ‘0’ or ‘5’. 5. A number is...

ARITHMETIC

INDEX

ARITHMETIC 1. BASICS............................................................... 2

2. L.C.M. AND H.C.F............................................. 8

3. RATIO AND PROPORTION............................ 11

4. PERCENTAGES................................................ 20 (PERCENTAGES GOLDEN RULES, DISCOUNT)

5. PROFIT AND LOSS.......................................... 33

6. AVERAGE.......................................................... 46

7. ALLIGATION..................................................... 55

8. SIMPLE INTEREST.......................................... 58

9. COMPOUND INTEREST................................. 64

10. RELATION BETWEEN CI & SI.................... 70

11. TIME AND WORK&PIPES AND CISTRENS 73

12. TIME AND DISTANCE................................... 87

13. BOATS AND STREAMS................................. 98

14. PROBLEMS ON AGES................................... 101

15. CLOCKS........................................................... 103

16. CALENDARS................................................... 106

17. MENSURATION-TWO DIMENTIONAL....... 108

18. MENSURATION -THREE DIMENTIONAL.. 116

www.OnlineIAS.com

+91-9246365622 www.KalyanIAS.com N. Kalyana Chakravarthy


ARITHMETIC

Type of Numbers

Whole numbers: The set of whole numbers is denoted by ‘W’ where ‘W’ = {0, 1, 2, 3, 4,5,………}

Natural Numbers: The numbers which are used to counting are known as natural

numbers or positive Integers. Their set is denoted by N. Thus. N = {1, 2, 3, 4,…………..}

Set of integers: All counting numbers, their negatives and ‘O’. When combined from the

set of integers. This is denoted by Z. Thus Z = {…………….. -3, -2, -1, 0, 1, 2, 3,………..}

Even numbers: The numbers which are exactly divisible by 2 are known as even

numbers. For example 2, 4, 6, 8,

Odd numbers: the numbers which are not exactly divisible by 2 are called odd numbers.

Ex: - 1, 3, 5, 7, 9,

Prime numbers: “A number is said to be a prime number. If its factors are ‘1’ and the

number itself only. Ex: - 2, 3, 5, 7, There are 25 prime numbers below 100.

Composite Numbers: The numbers which are not prime and other than are called

“composite numbers”. Ex: 4, 6, 8, 9, 12,

Rational numbers: A number of the form a/b where a,b are integers and relatively prime

to each other 0b is called a rational numbers.

0,,/ aZba

b

aQ

Irrational numbers: The numbers whose exact value can not be determined are called

Irrational numbers. Ex: .......................,7,5,3

Real numbers: Both rational and irrational numbers are collectively known as realnumbers.

1. BASICS

www.OnlineIAS.com



ARITHMETICTest of Divisibility:

1. A number is divisible by 2, if its unit’s digit is ‘0’ or even.

2. A number is divisible by 3, if the sum of the digits can be divided by 3.

3. A number is divisible by 4, if the number composed of the lost two digits can be divided

by 4 or the last two digits are zeros.

4. A number is divisible by 5. If the last digit is either ‘0’ or ‘5’.

5. A number is divisible by 6, if it is divisible by both 2 and 3.

6. A number is divisible by 8, if the number composed of the last three digits can be

divided by 8 or the last three digits are zeros.

7. A number is divisible by 9, if the sum of the digits can be divided by 9.

8. A number is divisible by 11, if the sum of the digits in the odd places of the number and

the sum of the digits in the even places are equal or the difference of these two sums

is divisible by 11.

9. A number is divisible by 12, if tit is divisible by both 3 and 4.

10. A number is divisible by 25, if it ends in ‘25’, ’75’, ‘00’.

Fraction: A fraction is a part of something m/n means considering m parts out of n parts.

Proper Fraction: when the numerator is less than the denominator, then the fraction is said

to be a proper fraction. For example 2/3, 4/6, 5/7,

Improper fraction: when the numerator is greater than the denominator then the fraction

is said to be an improper fraction. For example 15/4, 13/11, 3/2,

Mixed fraction: A mixed fraction consists of a whole number and a proper fraction. For

example 7 ¼ means where 7 is the whole part and ¼ is the fractional part.

www.OnlineIAS.com



ARITHMETICDecimal fraction: A fraction whose denominator is 10 or a multiple of 10 is called a

decimal fraction. For example 2/10, 4/100, 6/1000,

Vulgar fraction: A fraction whose denominator is other than 10 is called a vulgar fraction.

Ex: 2/7, 7/6, …………………..

Recurring decimal: In a decimal, some figure or a set of figures is repeated continually.

We call it a recurring decimal. Ex: 0.333………… 0.2454545……….

The set of repeated figures is called a period. We denote the recurring decimal by putting a

bar or a dot on the period. 3.0......................333.0 452.0......................2454545.0 Properties of perfect square:

No perfect square should end with 2, 3, 7, and 8.No perfect square ends with an odd number of zeros.The perfect square consisting of (n-1) or n digits will have n/2 digits in their root where

being an even positive integer.Cube: If a number is multiplied 3 times by itself then the resulting number is called cube ofthe given number.

Ex: - 125 is called the cube of 5 and 5 is called the cube root.

Cubes of the numbers from 1 to 10

13 =1 43 =64 73 =343 103=100023 =8 53 =125 83 =51233 =27 63 =216 93 =729From above it follows that. When any no is cubed the units place will be as follows.

2 8 3 7 4 4 5 5 6 6 7 38 2 9 9 0 0BASIC LAWS OF INDICES

nmnm aaa , nn

n

baa

a)/( , 2

1aa , ,10 a if 0a , nnn abba )( , mnnm aba )(

nn aa /1 , nmn

m

aa

a ,n

nn

aaa

11

, aa 1

www.OnlineIAS.com



ARITHMETIC

Rule of SimplificationIn simplifying a problem, bar or Vinculum must be initially removed. After removing

Vinculum, other brackets must be removed in the order ( ), { }, [ ]. After removing

brackets, we have to use the operations in the other given by “BODMAS”.

B - Bracket,

O - Of,

D - Division,

M - Multiplication

A - Addition

S - Subtraction.

EXERCISE

1. 15.60 0.30 = ?a) 4.68 b) 46.8 c) 0.468 d) 0.0468 e) None

2. 0.0144 0.012 = ?a) 0.12 b) 0.012 c) 1.2 d) 12 e) None

3. 0.09 0.008=?a) 0.72 b) 0.072 c) 0.0072 d) 0.00072 e) None

4 If3420 7 then19 0.01

x x

a) 35/9 b) 18/7 c) 63/5 d) 54/3 e) None

5. If17.28 200 then3.6 0.2

x x

?

a) 120 b) 12 c) 1.2 d) 0.12 e) None

6. 20 8 0.5 12 then20

xx

?

a) 2 b) 8 c) 18 d) 12 e) None

7. 0.50.1515 ?

a) 4.5 b) 45 c) 0.45 d) 0.03 e) None

www.OnlineIAS.com



ARITHMETIC

8. If 12276÷155=79.2 the value of 122.76÷15.5 isa) 0.792 b) 7.92 c) 79.2 d) 792 e) None

9. 3 5If 5 2.24 the value of is2 5 0.48

a) 0.168 b) 1.68 c) 16.8 d) 168 e) None

10.5If 15 3.88 then the value of is3

a) 0.43 b) 1.89 c) 1.63 d) 1.29 e) None11. If 28.05 2.55 1100 then 280.5 25.5 is equal to

a) 1.01 b) 1.1 c) 0.11 d) 11 e) None

12. 2 20.1 0.011 is equal to

0.0001

a) 100 b) 101 c) 1010 d) 1101 e) None

13. 0 .2 3 0 .0 2 3.0 0 2 3 2 3

?

a) 0.207 b) 207 c) 2072 d) 0.0207 e) None

14. If0.11 106, then

106x x

?

a) 2.56 b) 1.76 c) 0.256 d) 2.365 e)None

16. If 1.5 0.04 then the value of isy x

x yy x

a) 730/77 b) 73/77 c) 7.3/77 d) 0.73/77 e) None

17 0.6 0.7 0.8 0.3

a)32

10 b)32

100 c)223 d) 2.35 e) None

18. The value of 4.12 is

a)11499 b)

11490 c)

259 d)

359 e) None

19. 171 19 9=? a) 0 b) 1 c) 18 d) 81 e) None

20. 5005 - 5000 10 a) 0.5 b) 50 c) 5000 d) 4505 e) None

www.OnlineIAS.com



ARITHMETIC21. 3120 26 13 30

a) 2400 b) 3900 c) 546 d) 6547 e) None22. 8 4 3-2 4 3 7

a) -3 b) -4 c) 4 d) 5 e) None

23.48-12 3+912 9 3

a) 3 b) 21 c)7/3 d) 1/3 e) None

24. 7 7 7 75 5 5 5

a) 1 b) 1/5 c) 15/11 d) 3/11 e) None

25.17.28 23.6 0.2

x

a) 120 b)1.20 c) 12 d) 0.12 e) None

26. 10 9 8 7 6 5 equal to

a) 5 b) 1 c) 3 d) 9 e) None

271 1 13 4 104 6 4

x then x

a)126 b)

143 c)

113 d)

123 e) None

28348 is what part of

112

a) 3/7 b) 1/12 c) 4/3 d) 6/5 e)None

29 How may1 '8s are there in

1 372

a) 300 b) 400 c) 500 d) 200 e)None

ANSWERS FOR BASICSEXERCISE

1) a 2) c 3) d 4) d 5) d 6) c 7) a 8) b 9) b 10) d 11) d 12) a 13) e 14) d

15) a 16) b 17) c 18) b 19) d 20) d 21) d 22) c 23) d 24) d 25) c 26) c 27) d 28) d

29) a

www.OnlineIAS.com



ARITHMETIC

Factors and Multiples: If a number ‘m’ divides another number ‘n’ exactly, then ‘m’ iscalled the factor of ‘n’ is called the multiple of ‘m’

H.C.F.(Highest Common Factor): The H.C.F of two or more numbers is the greatestnumber that divides each one of the numbers exactly (fully).

Ex:- Hence H.C.F of 24 and 36 is 6.

18 and 54 is 18

If H is H.C.F of two numbers ‘a’ and ‘b’ then H divides ‘a’ and H divides ‘b’ G>C>F iaalso called G.C.D or G.C.M.

Co-primes : If the HCF of two numbers is one then the numbers are said to be co-prime. Ex: 10 and 21, 12 and 17 etc.

Co-prime need not be prime numbers.

L.C.M ( Least Common Multiple) : The least number which is exactly divided byeach one of the given numbers is called their L.C.M. Here each number should dividedthe L.C.M.

Ex: L.C.M of 20, 30 and 40 is 120

L.C.M. of co-primes is the product of the numbers.

H.C.F. always divides L.C.M of Fractions.

Important formula

Product of two numbers = (Their H.C.F)X(Their L.C.M)Ex: From the above examples product of numbers 30 72 2160 Their H.C.FXL.C.M 6 360 2160 H.C.F and L.C.M when numbers are given in fraction form

(i) H.C.F of fractions =H.C.F of Numerators

L.C.M of Denominators

(ii) L.C.M of fractions =L.C.M of Numerators

H.C.F of Denominators

2. L.C.M and H.C.F

www.OnlineIAS.com



ARITHMETICEXERCISE

1. H.C.F of1 2 3 4, , ,2 3 4 5 is

a) 1 b) 12 c) 1/5 d) 1/60 e) None of these

2. H.C.F of3 6 9, ,7 5 2 is

a) 3/70 b) 18 c) 81/35 d) 35/81 e) None of these

3. H.C.F of1 3 5 7 9, , , ,2 4 6 8 10 is

a) 1/120 b) 1/2 c) 1/10 d) 9/120 e) None of these

4. L.C.M of3 6 9, ,4 7 8 is

a) 3 b) 18 c) 3/56 d) 9/28 e) None of these

5. L.C.M of2 4 5 7, , ,3 9 6 12 is

a) 140/3 b) 35/9 c) 1/36 d) 1/18 e) None of these

6. L.C.M of2 5 4, ,3 6 9 is

a) 20/81 b) 1/18 c) 20/3 d) 5/9 e) None of these7. Which of the following fraction is greatest

a) 7/8 b) 6/7 c) 5/6 d) 4/5 e) None of these8. Which of the following is an ascending order

a)5 7 9, ,7 8 11 b)

5 9 7, ,7 11 8 c)

7 5 9, ,8 7 11 d)

9 7 5, ,11 8 7 e) None of these

9. Which of the following fraction is smallesta) 1/2 b) 3/7 c) 3/5 d) 4/9 e) None of these

10. Which of the following is in descending order ?

a)3 5 7, ,5 7 9 b)

7 5 3, ,9 7 5 c)

5 7 3, ,7 9 5 d)

7 3 5, ,9 5 7 e) None of these

11. Let a,b are two numbers. Their H.C.F is 4 , L.C.M is 42. Then which of the following is

true

a) Only one pair (a,b) exists b) Two such pairs (a,b) exists

c) Many such pairs (a,b) exists d) No such pairs (a,b) exists e) None of these12. The H.C.F of three numbers is 12. If these are in the ratio 1:2:3 then the numbers are

a) 4 : 8 : 11 b) 6 : 12 : 18 c) 8 : 16 : 24 d) 12 : 24 : 36 e) None of these

www.OnlineIAS.com



ARITHMETIC13. The product of two numbers 4444 and their H.C.F is 11, Then their L.C.M of the

numbers isa) 44 b) 404 c) 48884 d) 1111 e) None of these

14. The H.C.F of two numbers is 6 and their L.C.M is 78. If one of the numbers is 26 thenother numbers isa) 18 b) 2 c) 3 d) Not Exist e) None of these

15. The H.C.F of two numbers is 6 and their L.C.M is 72. If one of the numbers is 12 thenother numbers isa) 36 b) 24 c) 144 d) 60 e) None of these

16. The least perfect square number which is divisible by 3,4,5,6 and 8 isa) 900 b) 1200 c) 2500 d) 3600 e) None of these

17. The smallest number which is divisible by 12,15,20 and is a perfect square isa) 400 b) 900 c) 1600 d) 1300 e) None of these

18. The H.C.F and L.C.M of two numbers are 44 and 264 respectively. If the first number isdivided by 2, the quotient is 44. The other number isa) 33 b) 66 c) 132 d) 264 e) None of these

19. What least number must be subtracted from 1294 so that the remainder when divided by9,11,13 will leave in each case the same remainder 6a) 0 b) 1 c) 2 d) 3 e) None of these

20. The number of prime factor since the expression 10 17 276 .7 .11 isa) 54 b) 64 c) 71 d) 81 e) None of these

21. The total number of prime factors of the product 20 24 158 .15 .7 isa) 59 b) 98 c) 123 d) 138 e) None of these

22. The number of prime factor in 222 333 5552 .3 .5 isa) 3 b) 1107 c) 1110 d) 1272 e) None of these

23. Three measuring rods are 64 cm, 80 cm, and 96 cm in length. The least length of cloththat can be measured exact number of times using any one of the above rods isa) 0.96 m b) 19.20 m c) 9.60 m d) 96 m e) None of these

24. The traffic lights at three different road crossing change after every 48 sec, 72 sec 108sec respectively. If they all change simultaneously at 8:20:00 hours, then they will againchange simultaneously ata) 8:27:12 hrs b) 8:27:24 hrs c) 8:27:36 hrs d) 8:27:48 hrs e) None of these

ANSWERS FOR L.C.M AND H.C.F

EXERCISE

1) d 2) a 3) a 4) b 5) a 6) c 7) a 8) b 9) b 10) b 11) d 12) d 13) b 14) a

15) a 16) d 17) b 18) c 19) b 20) b 21) c 22) c 23) c 24) e

www.OnlineIAS.com



ARITHMETIC

Ratio: Comparison of two quantities in same units is called ratio. Thus the ratio between Rs.10 and Rs.5 is 10:5 or 2:1. The ratio is a constant. It has no units. The ratio can beexpressed in the form of a fraction also thus a:b is also denoted by a/b. In the ratio a:b; ais called antecedent and be is called consequent.

In the ratio if both antecedent and consequent are multiplied or divided by a constant K,The ratio is not changed.

Formula: Derive Ratios from a:b

1. Duplicate ratio = 22 : ba

2. Triplicate ratio = 33 : ba

3. Sub Duplicate ratio = ba :

4. Sub Triplicate ratio = 33 : ba

5. Inverse ratio of a:b is b:a

6. Compound ratio of a:b and c:d isdb

ca

or bdab :

Proportion : If two ratios are equal, then the four terms are said to be in proportion. Thus ifa:b = c:d, then the terms a, b, c, d are in proportion. In this case, the terms a and d arecalled ‘extremes’ or ‘ends and b and c are called ‘means’ And also the product of ends isequal to product of means, thus ad=bc, we can assume.b=ar, c=ar2, d=ar3 in same cases.

If a:b = c:d then1. a/b = c/d

2. b/a = d/c

3. a/c = b/d

4.dc

dc

ba

ba

Then lost relation is called compendo and dividend useful in solving some problems.

1. The mean proportional of a and b is ab

2. The third proportional of a and b is b2/a3. The fourth proportional of a, b and c is bc/a

3. RATIO and PROPORTION

www.OnlineIAS.com



ARITHMETIC4. If two terms are in a:b and x added to each term of the ratio and new ratio is c:d, then last

term isbcad

dcxa

)(

EXERCISE – 11. If A:B=2:3 and B:C=4:5 then A:C equals

a) 15 : 8 b) 8 : 15 c) 5 : 8 d) 8:5 e) None of these

2. If A : B = 7 : 9 and B : C = 3 : 5 then A : B : C is

1) 2 : 9 : 5 b) 21 : 35 : 45 c) 7 : 9 : 15 d) 7 : 3 : 15 e) None of these

3. If A=B/3 and B = c/2 then A : B : C is

a) 1 : 3 : 6 b) 2 : 3 : 6 c) 3 : 2 : 6 d) 3 : 1 : 2 e) None of these

4. If A : B = 2 : 3, B : C = 4 : 5, C : D=6 : 7 then A : D is

a) 2 : 7 b) 7 : 8 c) 16 : 35 d) 4 : 13 e) None of these

5. If a/b = 2/3 and b/c = 4/5 then (a+b) : (b+c) =?

a) 20 : 27 b) 30:13 c) 40: 51 d) 15: 19 d) None of these6. If a:b = c:d then b:d = ?

a) d:a b) a:c c) b:a d) a:b e) None of these

7. If a:b = c:d = e:f = 1:2 then (ma+nc+pe): (mb+nd+pf) = ?

a) 3:2 b) 1:2 c) 2:3 d) 1:3 e) None of these

8. If a/2=b/3=c/5 then (a+b+c)/c=?

a) 1 b) 4 c) 2 d) 4 e) None of these

9. If 10% of x is the same as 20% of y, then x : y is equal to


10. If 20% of x is the same as 30% of y, then x:y is equal to


11. Two numbers are in the ratio 3:5. If each number is increased by 10, the ratio becomes5:7 . The numbers are

a) 3, 5 b) 6, 10 c) 112, 20 d) 15, 25 e) None of these

www.OnlineIAS.com



ARITHMETIC12. If two-third of A, one-fourth of B and three-fifth of C are equal, then A:B:C is equal to

a) 9:24:30 b) 9:24:10 c) 18:24:10 d) 18:24:30 d)None of these

13. Two numbers are in the ratio 4:5. If each number is increased by 15, the ratio becomes6:7 . The first number is


14. The ratio of milk and water in a mixture of 84 litres is 3:4. What will be the new ratio if 3litres each of milk and water is added to the mixture ?


15. The ratio of numbers of boys and girls of a school with 504 students is 13:11. What willbe the new ratio if 12 more girls are admitted ?


16. Incomes of A and B are in the ratio 3:2 and their expenditure are in the ratio 5:3. If theysave Rs 800 each, find A’s income

a) Rs 4800 b) Rs 2400 c) Rs 1200 d) Rs 5000 e) None of these

17. A mixture of 140 litres contains milk and water in the ratio 3:4. How many litres of milkmust be added to mixture so as to make the ratio 5:4

a) 20 litres b) 40 litres c) 25 litres d) 30 litres e) None of these

18. Ratio of milk and water in a mixture 4:1. If 5 litres of milk is added in the mixture, newratio becomes 5:1. The quantity of milk in the mixture originally was:


19. Students in class I, II and III of a school are in the ratio 3:5:8. Has 15 more studentsadmitted to each class, the ratio would have becomes 6:8;11. How many total studentswere there in the beginning ?


20. Ratio between the annual income of A and B is 9:8 and between their expenditure is 8:7.If they save Rs 1000 each. Find A’s annual income.


www.OnlineIAS.com



ARITHMETIC21. The ratio of males and females in a group is 3:2. How many females must join the group

so that the ratio becomes 1:1, if there were 390 members originally ?


22. The ratio of boys and girls in a class of 160 students is 5:3. How many more girls shouldjoin the class to make the ratio 1:1?

‘ a) 20 b) 40 c) 15 d) 25 e) None of these

23. 264 litres of mixture contains milk and water in the ratio 8:3. How much water must beadded to the mixture so as to make the ratio of milk and water 2:1?


24. The mean proportional between 0.32 and 0.02 is

a) 0.34 b) -28 c) 41 d) -31 e) None of these

25. The weight of a 13 m long iron rod is 23.4 kg. The weight of 6 m long of such rod will be

a) 16.8 b) 12.4 c) 10.8 d) 12.6 e) None of these

26. The ratio of two numbers is 3:4 and their sum is 420. The greater of two numbers is


27. If the sum of two numbers is 65 and their difference is 13. Find the ratio between thenumbers


28. Sum of two numbers is 96 and difference between the numbers is 16. Find the ratiobetween the numbers.


29. The sum of two numbers is twice the difference between them. If the smaller number is20, find the bigger number.

a) 50 b) 30 c) 40 d) 60 d) None of these

30. A bag contains 25 paisa, 10 paisa and 5 paisa coins in the ratio 1:2:3. If their total valueis Rs 30, the number of 5 paisa coins is


www.OnlineIAS.com



ARITHMETIC31. The monthly salary of A,B,C is in the proportion of 2:3:5. If C’s monthly salary is Rs 1200

more than that of A, then B’s annual salary is


32. Three friends divide Rs 624 among themselves in the ratio ½ : 1/3 : 1/4. The share of thethird friend is


33. In a class, the number of boys is more than the number of girls by 12% of the totalstrength. The ratio of boys to girls is


34. A circle and a square have same area. Therefore, the ratio of the side of the square andthe radius of the circle is

a) 7 : 22 b) 22 : 7 c) 31 : 7 d) 7 : 31 5) None of these

35. The right cylinder and a right circular cone have the same radius and the same volume.The ratio of the height of the cylinder to that of the cone is

a) 6, 16 b) 8, 12 c) 4, 24 d) 4, 78 5) None of these

36. If 18:x = x::8, then x is equal to

a) 2 b) 3 c) 4 d) 9 5) None of these

37. The prices of a scooter and a television set are in the ratio 3:2. If a scooter costs Rs 6000more than the television set, the price of the television set is

a) Rs. 15000 b) Rs. 12500 c) Rs. 13000 d) Rs. 12000 5) None of these

38. A certain amount was divided between Kavita and Reena in the ratio 4:3 . If Reens’sshare was Rs 2400, the amount is


39. The ratio of money with Ram and Gopal is 7:17 and that with Gopal and Krishna is 7:17.If Ram has Rs 490, Krishna has


40. The students in three classes are in the ratio 2:3:5. If 20 students are increased in eachclass, the ratio changes to 4:5:7. The total number of students before the increase were

a)10 b)90 c)100 d) 250 e) None of these

www.OnlineIAS.com



ARITHMETIC41. 729 liters of a mixture contains milk and water in the ratio 7:2. How much more water is to

be added to get a new mixture containing milk and water in the ratio of 7:3


42. Rs 1050 id divided among P, Q and R. The share of P is 2/5 of the combined share of Q andR. Thus, P gets


43. 15 litres of a mixture contains 20% alcohol and the rest water. If 3 litres of water be mixedin it, the ratio of alcohol in the new mixture will be


44. In a mixture of 60 litres, the ratio of milk and water 2:1. What amount of water must beadded to make the ratio 1:2.


45. The ratio between two numbers is 3:4 and their L.C.M is 180. The sum of the numbers is


46. The ratio between the ages of kamala and Savitri is 6:5 and the sum of their ages in 44years . The ratio of their ages after 8 years will be


47. The ratio between Sumit’s and Prakash’s age at present is 2:3. Sumit is 6 years youngerthan Prakash. The ratio of Sumits age to Prakash’s age after 6 years will bea) 1 b) -1 c) d) 3 e) None of these

48. Rs 680 has been divided among A,B,C such that A gets 2/3 of what B gets and B gets ¼of what c gets. Then B’s share is


49. The incomes of A and B are in the ratio 3:2 and their expenditures in the ratio 5:3. If eachsaves Rs 1000, A’s income is

a) 11, 14 b) 10 ,16 c) 9, 17 d) 8,18 e) None of these

50. Two numbers are in the ratio 3:4, If 20 is subtracted from each of them, the ratio becomes2:3. What was the smaller number ?

a)40 b)60 c) 30 d) 20 e) None of these

www.OnlineIAS.com



ARITHMETIC51. 40 liter of a mixture contain milk and water in the ratio 3:2. If 8 liters of water is added to

it, What will be the ratio of milk and water in the final mixture


52. In a class, boys and girls are in the ratio 2:3. If 12 more girls join the class, The ratiobecomes 2:5. What is the number of boys in the class ?


53. There are 237 students in a school. If 3 boys and 14 girls left the school, then boys andgirls will be in the ratio 27:28. What is the number of girls in the school


54. In a theater, I, II and III class ticket rates are in the ratio 7:5:4 and the number of seats inthese classes are in the ratio 8:6:3. If the total collection of a “houseful” show is Rs.4,410, how much is realized by the sale of III class ticket ?


55. Three numbers are in the ratio 3:5:2 so that the sum of their squares is 342. What is thefirst number


56. Three numbers in the ratio 1:2:3 such that the sum of their squares is 5,600. What is theleast number


57. What number must be added to the numbers 3, 17, 26 and 86 so that the resultantnumbers will be in proportion


58. What number should be subtracted from the numbers of 12,26, 35 and 95 so that theyshould become proportional to each other ?


59. 4 books cost as much 3 pens, 8 pens cost as much as 5boxes, 12 boxes costs as muchas 20 bags. If the cost of each bag is Rs. 32. What is the cost of a book


www.OnlineIAS.com



ARITHMETIC60. Rs. 3,800 is divided among A, B and C so that A receives 3/ 16as much as B and C

together get. B receives 4/15 as much as A and C together receives. What is the share ofC


61. 3 doctors earn as much as 4 engineers, 5 engineers earn as much as 9 lawyers, 18lawyers earn as much as 30 contractions. If a contractor earn Rs. 12,000 per month.What is the earning of a doctor


62. If a carton containing a dozen eggs is dropped, which of the following cannot be the ratioof broken eggs to unbroken eggs


63. If a carton containing a two dozen mirrors is dropped, which of the following can be ratioof broken mirrors to unbroken mirrors ?


64. If the ratio of boys and girls in a class is 9:2, which of the following cannot be the totalnumber of students in the class ?


65. A mixture of 72 litres contains milk and water in the ratio 5:4. On adding some water inthe mixture the ratio becomes 2:3, find the quantity of water added to the mixture.


66. A mixture of 80 litres contains milk and water in the ratio 5:3. How many litres of milkmust be added to the mixture so that the ratio becomes 2:1 in the resultant mixture?


67. A mixture of 100 litres contains milk and water in the ratio 3:2. On adding some water inthe mixture the ratio becomes 2:3, find the quantity of water added to the mixture.


68. The ratio between two numbers in 5:8. If 8 is subtracted from both the numbers, the ratiobecomes 1:2. The original numbers are :

a) 10, 14 b) 29, 31 c) 40, 64 d) 20, 32 e) None of these

www.OnlineIAS.com



ARITHMETIC69. A vessel contains milk and water in the ratio 5:2. Had it contained 2 litres more of milk

and 2 litres less of water , the ratio would have becomes 4:5. What is the quantity of milkin the vessel?


70. Two Vessels A and B contain milk and water in the ratio 5:3 and 8:7 respectively. Find theratio in which the quantities be taken from the vessels so that the ratio of milk and waterin the new mixture is 13:10.


71. Two Vessels A and B contain milk and water in the ratio 7:3 and 3:2 respectively. Find theratio in which the quantities be taken from the vessels so that the ratio of milk and waterin the new mixture is 2:1.


72. Two Vessels contain mixture of milk and water in the ratio 5:2 and 3:1 respectively. Findthe ratio of milk and water in the new solution, if two mixture are mixed in equal amount.

a) 40:37 b) 60:21 c) 41:15 d) 15:48 e) None of theseANSWERS FOR RATION and PROPORTION

EXERCISE - 1

1) b 2) c 3) a 4) c 5) a 6) b 7) b 8) c 9) b 10) d 11) d 12) b 13) e 14) a

15) a 16) c 17) b 18) d 19) b 20) a 21) c 22) b 23) c 24) e 25) c 26) e 27) b 28) b

29) d 30) e 31) e 32) e 33) a 34) b 35) e 36) e 37) d 38) e 39) e 40) c 41) e 42) c

43) a 44) a 45) e 46) d 47) 48) e 49) 50) a 51) a 52) e 53) e 54) e 55) a 56) d

57) b 58) e 59) a 60) 61) a 62) 63) a 64) c 65) b 66) b 67) a 68) d 69) e 70) e

71) d 72) e

www.OnlineIAS.com



ARITHMETIC

Percent : Percent means a hundredth part. ‘x’ percent means ‘x’ parts out of 100 and isdenoted by x%

To express x% as a fraction : x% = x/100

To express a fraction as a percent : a/b=(a/b × 100)%Thus, 15% = 15/100 = 3/20 and 4/5 = ( 4/5 × 100) = 80%Formula:

1. If A is x% more than B, then B is %100

100

x

x less than A.

2. If A is x% less than B, then B is %100

100

x

x more than A.

EXERCISEConvert percent into a fraction or decimal

1. 25% of 75% of 80 =?


2. What rate percent is 1 minute 12 seconds to an hour?

a) 3% b) 2% c) 5% d) 6% e) None of these

3. The population of a town is increase from 25000 to 30000 in a year. Find the rate ofincrease.


4. If rate of income tax is increased from 20% to 25%. Find the additional amount of tax, aperson has to pay, if his total income is Rs. 40000.

a) Rs 3000 b) Rs 2000 c) Rs. 25000 d) Rs. 35000 e) None of these

5. Salaries of A and B are in the ratio 3:4. Both of them spend 75% of their salaries and sverest of the money, Find the ratio of their savings.

a) 3:4 b) 4:3 c) 1:1 d) Can’t say e) None of these

6. In an examination every candidate took Maths or English or both. If 65% took Maths and60% English, how many took Maths and English both?


4. PERCENTAGES

www.OnlineIAS.com



ARITHMETIC7. In a group of students, 70% can speak English and 75% can speak Hindi. If 10% of the

students can speak non of the two languages, what percentage of students can speakboth the languages ?


8. 1300 boys and 700 girls appeared in an examinations, 80% of the boys and 70% of thegirls passed in the exam, find the total percentage of failed students,

a) 25.5% b) 2.52% c) 2.55% d) 23.5% e) None of these

9. The prices of sugar and rice are in the ratio 4:5. If the price of sugar is increased by 10%and that of rice by 20%, find the ratio between increased prices of sugar and rice.


10. If 30% of a number is 90, the number is :


11. 20% of 30% of a number is 12, the number is


12. 15 litres of a mixture contains 20% alcohol and rest water, IF 3 litres of water is added init, Percentage of alcohol in the new mixture will be ?

a) 15.54% b) 16.67% c) 14.55% d) 18.46% e) None of these

13. In an examination, a student has to secure 40% of the maximum marks to pass. Onestudent got 40 marks and failed by 40 marks. The maximum marks in the examinationare:


14. A student has to secure 40% marks in an examination to qualify. He gets 120 marks andfails by 80 marks. The maximum marks are :


15. A student gets 29% marks in an examination but fails by 24marks. If the pass percentageis 35%, the maximum marks are.


16. Two students A and B appeared in an examination. If A secured 9 marks more than B andhis marks are 56% of sum of their marks, find marks obtained by A.


www.OnlineIAS.com



ARITHMETIC17. A student got 42% marks and has secured 12 marks more than the minimum passing

marks another student who got 45% has obtained 30 marks more than the minimumpassing marks. The maximum marks are:


18. A student gets 35% marks and fails by 10 marks and another student who gets 31%marksfails by 30marks. The maximum marks are:


19. A student gets 30%marks and fails by 20 marks and another student who gets 35%marks, gets 10 marks more then minimum passing marks. The maximum marks are:


20. In an examination, a student gets 38% of the maximum marks and fails by 6 marks.Another student who gets 45%of the maximum marks, gets 15marks more than therequired passing percentage. Find passing percentage of the marks.

a) 39% b) 40% c) 44% d) can’t say e) None of these.

21. A student scores 37% marks and fails by 12 marks and another student who scores 42%marks and got 8 marks more than the minimum passing marks. The passing percentageis:


22. A person saves 10% of his income. If his income is increased by 20% and he saves15% of the new income, by what percent his savings will increase ?


23. A fruit seller sells 30% apples and still has 630 apples in the stock. How many appleshad he bought ?


24. A man spends 20% of his income on food and 70% on clothing. If he still has a balanceof Rs. 200, what is his total income ?

a) Rs. 100 b) Rs. 200 c) Rs. 1000 d) Rs. 2000 e) None of these

25. If a man after spending 97% of his income, saves Rs.300 per month, his annual incomeis:

a) Rs.10000 b) Rs.12000 c) Rs. 36000 d) Rs. 120000 e) None of these

www.OnlineIAS.com



ARITHMETIC26. In an election contest between A and B, A wins by the margin of 240 votes. If A gets 60%

of the total votes, total votes are:


27. If 20% of 250+25% of x=100, then x= ?


28. 60% of 2300=30% of ?


29. If 20% of a number is equal to 25% of the other number, find ratio between the twonumbers.


30. In a town 40% of the male population and 45% of the female population are married. Findthe ratio between male and female population in the town assuming that one man marriesone woman and vice-versa.


31. population of a village is 90000,5/9th of them are males and rest are females. If 40% of themales are married, what is the percentage of married females ?


32. Total number of boys and girls in a school is 150. If the number of boys is x, the numberof girls is x% of the total number of students. The number of boys is :


33. If percent price of sugar after 10% reduction is Rs.18 per kg, find the original price ofsugar per kg.

a) Rs.1.80 b) Rs.10.82 c) Rs.16.20 d) Rs.20 e) None of these

34. Sum of 5% of a number and 9% of other number is equal to sum of 8% of first number and7% of the second number. Find ratio between the numbers.


35. If sum of 5% of a number and 9% of another number is equal to ¾ of sum of 8% of firstnumber and 11% of the second number. Find ratio between the numbers.

a) 1:4 b) 3:4 c) 4:3 d) 5;9 e) None of these

www.OnlineIAS.com



ARITHMETIC36. A number when decreased by 20% gives 80. The number is:


37. A number when increased by 25% gives 80. The number is;


38. When 40 is deducted from 40% of a number, the result is 40. the number is:


39. When 60% of a number is added to 60, the result is same number. The number is:


40. When 75% of a number is added to 75, the result is same number, the number is:

a) Rs. 400 b) Rs.500 c) Rs.225 d) Rs.1600 e) None of these

41. Price of an article is increased by 3%. Had it been Rs. 16 less, price would have beendecreased by 1% of the original price. Find original price of the article.

a) Rs 1600 b) Rs 800 c) Rs500 d) Rs 400 e) None of these

42. A man spends 10% of his income on food and 80% of the remaining income on clothing.If he still has a balance of Rs 180, what is his total income ?


43. A person gave 20% of his income to his elder son, 30% of the remaining to the youngerson and 10% of the balance to a trust. If he is left with Rs. 10080, his income was:


44. A man had some eggs. Out of them 10% had to be thrown away as they were broken.80% of the remaining eggs were sold and now he is left with only 90 eggs. How manyeggs had he in the beginning?


45. If A’s salary is 110% of B’s, B’s salary is 80% of C’s. Find C’s salary, if A’s salary is Rs.440.


www.OnlineIAS.com



ARITHMETIC46. A’s salary is 20% more than B’s, B’s salary is 10% less than C’s. If A’s salary is Rs.

1080, Find C’s salary.


47. In an examination, A gets 20% less marks than B, B gets 30% marks less than C. If Agets 112 marks, find marks obtained by C.


48. In an examination, 35% students failed in English and 30% in Math. If 10% studentsfailed in both subjects, students passed in both subjects are:


49. In an examination, 50% students failed English and 40% in Math and 15% studentsfailed in both subjects. If 200 students passed in both the subjects, find the number ofstudents appeared in the exam.


50. In an examination, 35% of the candidates failed in Maths and 25% in English while 15%failed in both subjects. How many candidates passed in one subject but or in the other?


51. In an examination, 60% of the candidates passed in English, 50% in Math and 20%failed in both the subjects, How many students passed in both the subjects?


52. In an examination, 60% of the candidates passed in English, 70% in Math and 40% inboth subjects. How many students failed in both subjects?


53. In an election contest between two candidates, 10% of total voters did not take part. Thecandidate who was elected got 60% of the votes casted. If he got 180 votes more than hisopponent, find total number of voters.


54. A reduction of 10% in the price of sugar enables a customer to buy 4kg. more of sugar forRs. 400. What is the reduced price per kg?


www.OnlineIAS.com



ARITHMETIC55. A reduction of 20% in the price of sugar enables a purchaser to buy 4 kg more of sugar for

Rs. 80. The original price of the sugar per kg. is:


56. A salesman receives salary of Rs. 4000 per month and 10% commission on total sales.What is his earnings, if sales is Rs. 9000?


57. A salesman receives salary of Rs. 5000 per month and 20% commission on total sales.What is the amount of sales, if his total earning in a month is Rs. 60000


58. A salesman receives a salary of Rs. 1000 per month and 10% commission on sales inexcess of Rs. 5000. What is the amount of sales, if he earns Rs. 2000 in a particularmonth?


59. Mohan’s income and expenditure are in the ratio 5 : 3. His income increased by 12% andexpenditure by 15%. By what percent does his savings increase?

a) 2% b) 7.5% c) 8% d) 6% e) None of these

60. Sohan’s expenditure and savings are in the ratio 3 : 2. His income increases by 12% andsavings by 15%. By what percent would his expenditure increase?


61. A mixture of 3 litres contains 20% alcohol and another mixture of 7 litres contains 30%alcohol. Find the strength of alcohol in the resulting mixture, if two mixtures are mixedtogether.

a) 45% b) 27% c) 30% d) 35% e) None of theseANSWERS FOR PERCENTAGES

1) c 2) b 3) b 4) b 5) a 6) e 7) 8) d 9) e 10) c 11) e 12) 13) e 14) e

15) c 16) c 17) d 18) b 19) a 20) b 21) c 22) d 23) c 24) d 25) d 26) c 27) b 28) b

29) d 30) 31) c 32) c 33) d 34) a 35) e 36) d 37) b 38) c 39) d 40) e 41) 42) b

43) d 44) d 45) c 46) e 47) e 48) b 49) b 50) 51) b 52) a 53) d 54) 55) c 56) d

57) b 58) c 59) b 60) d 61) b

www.OnlineIAS.com



ARITHMETIC

PERCENTAGE (GOLDEN RULES)

Formulae

1. The product of two or more numbers is increased by x% if one of the numbers is increaseby x%.

2. The product of two or more umbers is decreased by x% if one of the number is decreasedby x%.

3. If we have two numbers – one of them is increased by x% and the other is decreased byx%. Then, product o the numbers will be decreased by x2/100%

4. If out of two numbers first number is increased by x% and second number is increasedby y%. Then percent increase in the product of two number is x + y + xy/100

5. If out of two numbers first number is increased by x% and second number is decreasedby y%. Then percent increase or decreased in the product of two number is x - y - xy/100

a. If A’s income is 1/x more than B’s income,then B’s income is lessthan A’s income by1/(1+x).

b. If A’s income is 1/x less than B’s income, then B’s income is more than A’s income by1/(x-1).

EXERCISE

1. Price of a commodity is increased by 10% and then resultant price is decreased by 10%.Find net increase or decrease in the price.

a) 1% decrease b) 1% increase c) No effect d) 5% decrease e) None

2. selling price of a commodity is increased by 15% in a year and then the new price isdecreased by 15% in the next year. Find net increase or decrease in the selling price.

a) No effect b) 2% decrease

c)2.25% decrease d) 2.25% increase e) None

3. Price of sugar having been increased by 20%, a housewife reduced consumption of sugarby 20%. What was the effect of this on her expenditure on sugar ?

a) 4% decrease b) 4% increase c) no effect d) 1% decrease e) None

4. The salary of an employee is first increased by 20% and then again increased by 30%.Find percent increase in his salary from the original salary.

a) 6% b) 44% c) 50% d) 56% e) None

www.OnlineIAS.com



ARITHMETIC5. The salary of an employee is Rs.9870. It is first increased by 20% and then is

decreased by 10%. Find percent increase in his salary from the original salary.

a) 8% b) 10% c) 12% d) 13% e) None

6. The salary of an employee is first decreased by 10% and then is increased by 20%. Findpercent increase in his salary from the original salary.

a) 8% b) 10% c) 12% d) 13% e) None

7. Selling price of a commodity is increased by 20%. As a result of it, quantity sold isdecreased by 30%. What is effect of this on total sales?

a) 16% decrease b) 10% increase c) 10% decrease d) 50%increase e) None

8. The population of a city is decreased by 20% in a year. In the next year, the populationis again decreased by 30%. Find per cent decrease In population of the city from theoriginal population.

a) 44% b) 50% c) 55% d) 56% e) None

9. The selling price of a commodity is reduced by 25%. As a result, sale of the commodity(inunits) is increased by 20%.What will be the effect

a) 5% decrease b) 10% increase c) 45% increase d)10% derease e) None

10. The population of a city is decreased by 10% in a year. In the next year, the population isagain decreased by 30%. Find percent decrease in the population of the original population.

a) 35% b) 37% c) 40% d) 43% e) None

11. B’s income is 20% more than A’s and C’s income is 25% less then B’s. How manypercent C’s income more than A’s?

a) 5% b) 40% c) 45% d) 50% e) None

12. If B’s salary is 30% more than A’s and C’s salary is 20% less than B’s. How manypercent C’s salary is more than A’s ?

a) 4% b) 6% c) 8% d) 10% e) None

13. The price of a commodity was increased in the ratio 4:5. If a customer reduces itsconsumption in the ratio 4:3, how much per cent his expenditure in the commodity willincrease or decrease

a) 1% increase b) 1% decrease c) 6.25% increase d) 6.25% decrease e) None

www.OnlineIAS.com



ARITHMETIC14. Price of an article increases by 20%. As a result turnover increases by 12%. Find the

decrease in quantity sold.

a) 5% b) 6.67% c) 8% d) 16% e) None

15. A sells his goods 20% cheaper than B but 20% dearer than C. How much a customer ofB saves, if he buys goods from C for Rs. 100?

a) Rs. 4 b) Rs. 40 c) Rs. 44 d) Rs. 50 e) None

16. Price of a commodity is increased by 25%. By how much new price must be reduced torestore it the original price?

a) 20% b) 25% c) 33 1/3% d) 50% e) None

17. If A’s salary is 25% more than B’s, then how much percent is B’s salary less than A’s:

a) 20% b) 30% c) 25% d) 33 1/3% e) None

18. If price of oil is increased by 33 1/3%, by how much a housewife must reduce consumptionof so that her expenditure on oil remains the same?

a) 33 1/3% b) 25% c) 40% d) 50% e) None

19. If the price of coal is increased by 25%, by what percent the consumption of coal must bereduced so that the expenditure is not increased?

a) 20% b) 25% c) 33 1/3% d) 50% e) None

20. Price of a commodity is reduced by 10%. By how much, new price must be increased torestore it to the original price?

a) 10% b) 11% c) 9 1/11% d) 11 1/9% e) None

21. The difference between two numbers is 20% of the larger number. If the smaller number is40, the larger number is:

a) 32 b) 48 c) 50 d) 60 e) None

22. A’s income is 50% less than B’s. By how many percent, B’s income is more than A’s.

a) 33.33% b) 50% c) 75% d) 100% e) None

23. Price of cloth having been raised by 75%, by how much percent a householder mustreduce his consumption of cloth so as not to increase his expenditure?

a) 42 6/7% b) 57 1/7% c) 75% d) 50% e) None

www.OnlineIAS.com



ARITHMETIC24. Price of cloth having been reduced by 75%, how much percent a householder can increase

his consumption of cloth so that her expenditure on the cloth remains the same?

a) 50% b) 75% c) 200% d) 300% e) None

25. If the price of sugar is increased by 50%, by how much percent a housewife must reducethe consumption of sugar so that her expenditure on sugar is increased by 20%only.

a) 10% b) 12% c) 20% d) 25% e) None

26. Price of admission ticket is reduced by 20%. As a result, total collection amount isincreased by 60%. Find percent increase in the sale of tickets.

a) 24% b) 40% c) 80% d) 100% e) None

27. If the price of a commodity is reduced by 20%. As a result , total collection amount isincreased by 60%. Find percent increase in the sale of tickets.

a) 80kg b) 81kg c) 99kg d) 100kg e) None

28. Price of sugar having been fallen by 10%, a consumer can buy 10kg, more of sugar thanwhat he was buying originally. Find the quantity he was buying originally.

a) 80kg b) 90 kg c) 100 kg d) 110kg e) None

29. Price of a commodity having been increased by 20%, a consumer can buy 10%kg. lessthan the quantity he was buying originally. Find the quantity he was buying originally.

a) 100 kg b) 90 kg c) 80 kg d) 60kg e) None

30. If price of sugar is fallen by 5%. A man can buy; 220kg. Find the quantity of sugar he wasbuying originally.

a) 242kg b) 240 kg c) 210 kg d) 209 kg e) None

31. If price of rice is increased by 10%, a housewife can buy 110 kg. rice fore a certainamount. Find quantity of rice she was buying at original price.


32. Price of sugar having been fallen by 10%, a consumer can buy 22 kg. more than before.Had the price been increased by 10%, how much quantity of sugar could he have boughtfor the same sum?


www.OnlineIAS.com



ARITHMETIC33. Income-tax rate is 20% in a particular year. If in the next year, a person’s income is

increased by 25% but total tax liability remaining the same, find tax-rate during the nextyear.

a) 10% b) 12% c) 20% d) 25% e) 16%

34. The income of a sales agent remains the same eve though the rate of commission isincreased from 4% to 5%. Find the percent decrease in the sales.

a) 9% increase b) 9% decrease c) 12% decrease d) 5% increase e) 20% decrease

35. The rate of income tax is increased from 4%to 5% as the result of it tax – liability of aperson is increased by 10%. Find percent increase or decrease in his income.

a) 5%increase b) 9%incease c) 9%decrease d) 12%decrease e) None

36. Rate of commission is increased from 9% to 10%, but due to decrease in sale amount byRs.1000, a selling agent got the same commission as in the last year. Find the amount ofsale achieved by him in the last year.

a) Rs. 8000 b) Rs. 9000 c) Rs.10000 d) Rs. 12500 e) None

37. A man’s income is increased by Rs.2000 in a year. Rate of income-tax having reducedfrom 25%to 20%, his tax-liability remains the same as in the last year. Find his income inthe current year.

a) Rs. 4000 b) Rs.5000 c) Rs.8000 d) Rs.10000 e) None

38. The population of a village is increased by 5% in one year and in the next year it isdecreased by 5%. If at the end of second year, the population is 39900, what was thepopulation at the beginning of first year?

a) 39000 b) 39500 c) 39800 d) 40000 e) None

ANSWERS FOR PERCENTAGE(GOLDEN RULES)

1) a 2) c 3) a 4) d 5) a 6) a 7) a 8) d 9) d 10) b 11) d 12) a 13) d 14) b

15) d 16) a 17) a 18) b 19) a 20) d 21) c 22) d 23) a 24) d 25) c 26) d 27) d 28) b

29) d 30) d 31) d 32) b 33) e 34) e 35) d 36) c 37) d 38) d

www.OnlineIAS.com



ARITHMETIC

DISCOUNTEXERCISE

1. Single discount rate equivalent to a series of discount of 20% and 25% is :

a) 5% b) 40% c) 45% d) 50% e) None

2. A TV whose catalogue price is Rs. 15000 is availabele at two successive discounts of 10%and 20%, find the single equivalent discount.

a) 25% b) 28% c) 30% d) 32% e) None

3. If A man allows 20% discount on all his articles, the number of the articles sold is increasedby 20%. What is the effect on total sale?

a) 40%increase b) 4%increase c) 4%decrease d) No effect e) None

4. Catalogue price of a TV is Rs. 10000. How much a customer need to pay, if two successivediscounts of 20% and 20% are available on the TV?

a) Rs. 6000 b) Rs.6200 c) Rs.6400 d) Rs. 6500 e) None

5. A watch whose list price is s. 500, si available at two successive discounts fo 10% and20% Amount paid by the customer is :


6. A man bought an article for Rs. 21. What was the marked piece of the article if the articlewas sold at 30% discount?

a) Rs. 30 b) Rs. 6.30 c) Rs. 14.70 d) Rs. 70 e) None

7. The price of an article is raised by 30% and then two successive discounts of 10% eachare allowed. What is net increase in the piece of article?

a) 5% b) 5.3% c) 10% d) 13% e) None

8. A shop keeper allows two successive discounts of 3% and 7% while another allows twosuccessive discounts of 2% and 8%. From which shopkeeper should a customer buy ifmarked price is same at both shops?

a) First b) Second c) Both are samed) Data Inadequate e) None

9. A shopkeeper allows two successive discounts on an article whose marked price is Rs.150 and selling price is Rs. 105. What is first discount if second is 12.5%?

a) 16.67% b) 17.5% c) 20% d) 25% e) None

ANSWERS FOR DISCOUNT:1) b 2) b 3) c 4) c 5) b 6) a 7) b 8) b 9) c

www.OnlineIAS.com



ARITHMETIC

By selling at a cost more then the cost price, a trader gets gain and by selling at a costless than the cost price, a trader losses. The profits and losses are calculated on lost price.Thus

Profit and losses can be expressed as percentages also.

Formula:1. Profit = selling price – cost price (SP>CP)2. Loss = Cost price – selling price. (SP<CP)

3. Profit % =

CP

Proft100

4. Loss % =

CP

Loss100

5. S.P =

100

%100 gainC.P

6. C.P =

%100

100

gain S.P

7. S.P =

100

%100 lossC.P

8. C.P =

%100

100

lossS.P

9. If SP’s of two articles are the same and the proft % on one is same as sthe loss % on the

other, then there will be a loss which is in %

100

%%

10.Two successive discounts of x% and y% are equivalent to a single discount % of

100

yxyx

.

5. PROFIT and LOSS

www.OnlineIAS.com



ARITHMETIC

EXERCISE1. If cost price and selling price of an article are Rs. 12 and Rs. 15 respectively, profit percentage is: a) 10% b) 20% c) 25% d) 33.33% e) None

2. An article costing Rs. 400 is sold at 20% profit .Find its selling price.


3. A shopkeeper bought a chair whose marked price is Rs. 800, at two successive of10% and 15% respectively. He spent Rs. 28 on its transporation and then sold thechair for Rs. 800. What is his gain in percentage?

a) 10% b) 20% c) 25% d) 40% e) None

4. An article costing Rs. 500 is sold at 10% loss. Find its selling price.


5. An article is sold for Rs. 900 and hence gaining 105 of the selling price. Find its costprice.


6. If selling an artijcle for Rs. 990 causes 10% loss on the selling price, find its costprice.


7. On selling an article for a certain amount, a man gains 20%. What is the profitpercent, if he sells the article for double the amount?

a) 10% b) 20% c) 40% d) 140% e) None

8. On selling an article for a certain price, a man loses 30%. What is the loss/profitpercent, if he sells the article for double the price?

a) 60%loss b) 15%loss c) 40%profit d) 30%profit e) None

9. A man gains 10% by selling an article for a certain price. what is profit/loss if thearticle is sold for half the price?

a) 45%loss b) 5% loss c) 5% profit d) 55% profit e) None

10. A retailer buys goods at 10% discount on its marked piece and sells them at 20%higher then the marked piece. What is his profit percent?

a) 20% b) 25% c) 30% d) 33.33% e) None

www.OnlineIAS.com



ARITHMETIC11. A dishonest merchant professes to sell his goods at cost piece, but uses a weight of

900 grams for one kg. weight. What is his profit percent?

a) 10% b) 11 1/9% c) 9 1/11% d) 11% e) None

12. A merchant professes to sell goods at the loss of 5% but uses weight of 900gramsin place of one kilogram. What is his profit percent?

a) 5% b) 5 5/9% c) 6% d) 10% e) None

13. A merchant professes to sell goods at 20% profit but uses weight of 800grams inplease of a kilo gram. What is his actual profit percent?

a) 20% b) 25% c) 50% d) 33.33% e) None

14. A shopkeeper buys some pens. If he sells them @ Rs. 13per pen, his total loss isRs.150 but on selling them @ Rs. 15 per pen, his total gain is Rs. 100. how manypens did he sell?

a) 100 b) 125 c) 150 d) 250 e) None

15. If selling price of a commodity is increased by Rs. 35, the profit is increased by 7%.Find cost price to the article.


16. A machine is sold at 20% profit. Had it been sold at 25% profit, it would have fetchedRs.35 more. The cost price of the machine is :


17. A machine is sold at a loss of 10%. Hard it been sold at a profit of 15%, it would havefetched Rs. 50 more. The cost price of the machine is:


18. Profit margin of a merchant is increased by 10%, if he sells an article for Rs. 650,instead of Rs. 600. What is the cost price of that article?


19. A bicycle is sold at 10% profit. Had it been sold for Rs. 10 less, the profit would havebeen 5% only. What is the cost price of the bicycle?


www.OnlineIAS.com



ARITHMETIC20. An article is sold at 10%loss. Had it been sold for Rs. 30 more, the loss would have

been 5% only. What is the cost price of the article?


21. On selling an article for Rs.600, a man gains 20% of the selling piece. Find profitpercentage on the cost price?

a) 20% b) 25% c) 30% d) 33.33% e) None

22. On selling an article for Rs. 250, a shopkeeper gains Rs. 50. His gain percent is:

a) 16.67% b) 20% c) 25% d) 33.33% e) None

23. On selling an article for Rs. 200, a man gains Rs. 20, then his loss percent is.

a) 10% b) 9 1/11% c) 11 1/9% d) 20% e) None

24. On selling an article for Rs. 20, a man loses Rs. 20, then his loss percentage is :

a) 20% b) 11 1/2% c) 9 1/11% d) 33.33% e) None

25. On selling an article for Rs 250, a shopkeeper loses Rs. 50. his loss percent is

a) 33.33% b) 25% c) 20% d) 33% e) None

26. Selling price of an article is Rs. 330. Find cost price of the article, if gain 10% oncost price.

a) Rs .280 b) Rs 300 c) 200 d) Rs 230 e) None

27. On selling an article for Rs 300, a shopkeeper gain 20% of the cost price, Find costprice of the article.

a) Rs .280 b) Rs 300 c) 200 d) Rs 230 e) 250

28. On selling an article for Rs. 900, a shopkeeper losses 10% of the cost price. Findcost price of the article.

a) Rs .1080 b) Rs 1300 c) 1200 d) Rs 1230 e) Rs 1000

29. If an article costing Rs. 1000 is sold gaining 20% of its selling price. Find selling priceof the article.

a) Rs .2820 b) Rs 1400 c) Rs.1300 d) Rs 1250 e) None

www.OnlineIAS.com



ARITHMETIC30. A retailer buys goods at 9/10 of its marked price and sells them at 12/10 of the

marked price, Find his profit percent.

a) 20% b) 11 1/2% c) 9 1/11% d) 33.33% e) None

31. A shopkeeper purchases goods at 19/20 of its marked price and sells them at 14%more than its marked price. Find his profit percent.

a) 10% b) 20% c) 40% d) 140% e) None

32. A shopkeeper buys articles at 10% discount and sells them at 35% higher than themarked price. What is his profit percentage ?

a) 30% b) 50% c) 20% d) 10% e) None

33. A merchant sold 20 kg of rice for Rs. 240 and thus earned profit equal to the cost priceof 4 kg. Find the cost price of rice per kg.

a) Rs . 20 b) Rs 10 c) Rs 300 d) Rs 1250 e) None

34. A man bought 25 kg of rice for Rs. 750. On selling them for a certain price, he sufferedloss equal to the selling price of 5 kg. Find the selling price of 1 kg of rice.

a) Rs .28 b) Rs 25 c) Rs 20 d) Rs 12 e) None

35. Some quantity of tea is sold at Rs. 22 per kg, making 10% profit. If total gain is Rs.88, what is the quantity of tea sold?


36. On selling an article for Rs. 550, a man gains 10%. What will be the selling price, ifdesired profit is 20%?

a) Rs . 200 b) Rs 100 c) Rs 300 d) Rs 1250 e) Rs. 600

37. On selling an article for Rs. 400, a man loses 20%. What will be the selling price, ifdesired profit is 10%?

a) Rs . 400 b) Rs 500 c) Rs 550 d) Rs 250 e) Rs.300

38. A merchant fixed selling price of his articles at Rs. 700 after adding 40% profit to thecost price, As the sale was very low at this price level, he decided to fix the sellingprice at 10% profit. Find the new selling price.


www.OnlineIAS.com



ARITHMETIC39. A shopkeeper bought some eggs at the rate of Rs. 16 per dozen, Due to mishandling

20% of the eggs bought were broken during the transpiration. At what rate of perdozen should he sell the remaining eggs so as to gain 30% on the total cost price?


40. A trader buys apples at 7 apples for a rupee and sells them at 40% profit. How manyapples does he sell for a rupee?

a) 6 b) 5 c) 4 d) 3 e) 1

41. A man purchases 5 pens for a rupee. How many pens should he sell for a rupee if hewants to earn 25% profit?

a) 6 b) 5 c) 4 d) 3 e) 1

42. On selling apples at 36 for a rupee, a shopkeeper loses 10%. How many applesshould he sell for a rupee in order to gain 8%

a) 30 b) 15 c) 20 d) 35 e) 10

43. On selling 7 pens for Rs. 44, a man gains 10% of the cost price, what should be theselling price of 10 pens of 10 pens, if desired profit is 40%.


44. A man sells eggs @ 10 eggs for 7 rupee, gaining 30%. How many eggs did he buy for7 rupee?

a) 7 b) 11 c) 13 d) 15 e) None

45. On selling an article for Rs. 600, a man gains 20%. What will be the profit if the articleis sold for Rs.800?

a) 60% b) 50% c) 40% d) 30% e) None

46. On selling an article for Rs. 630, a man loses 10%. What will be his profit if the articleis sold for Rs.749?

a) 5% b) 6% c) 7% d) 8% e) None

47. On selling an article for Rs. 50, a man loses 1/6 of his outlay. Find his profit percentage,if the article is sold for Rs. 66.

a) 5% b) 10% c) 20% d) 25% e) None

48. On selling an article for Rs. 64, a man gains 1/7 of his outlay, Find his profit percentage,if the article is sold for Rs. 63.

a) 12.5% b) 20% c) 25% d) 33.33%

www.OnlineIAS.com



ARITHMETIC49. A bought a pen for Rs.200 and sold it to B at 10% gain. B sold it to C at 20% loss and

C sold it to D at 25% gain. What was the piece paid by D?

a) Rs. 180 b) Rs.200 c) Rs. 220 d) Rs. 225 e) None

50. A manufacturer sells a TV at 10% profit to a wholesaler who in turn sells it to a retailerat 20% profit. If the price paid by the retailer is Rs. 13200, how much the TV costs tothe manufacture?


51. A sells an article to B at a profit of 20%. B sells it is to C at a profit of 30%. If C haspaid Rs.780, the cost price of the article to A is:

a) Rs.350 b) Rs. 390 c) Rs. 400 d) Rs.500 e) None

52. A watch is sold at 10% discount on its marked price of Rs. 480. If the retailer makes20% profit on the cost price, find the cost price of the watch.


53. A shop keeper allows 25% discount on the marked price of his articles and hencegains 25% of the cost Price. What is the marked price of the article on selling whichhe gains Rs.120?

a) Rs. 400 b) Rs.600 c) Rs, 800 d) Rs.1000 e) None

54. A man bought a horse for Rs. 10000 and sold it to B at 10% profit and B sold it to C at10% loss. Find the amount paid by C.

a) Rs.10000 b) Rs.9900 c) Rs.9999 d) Rs. 11000 e) None

55. A man purchased two articles for total cost of Rs.9000. He sold the first article at 15%profit and the second at 12% loss. In the bargain, he neither gained nor lost anything.Find cost price of the first article.

a) Rs.4000 b) Rs.4500 c) Rs.5000 d) Rs.5500 e) None

56. A man purchased two articles for Rs. 10000 each. On selling first, he gains 20%andon the other, he loses 20%. What is profit/loss in the transation?

a) 4%loss b) 4%gain c) 2%loss d) No profit/loss

57. A man sold two articles for Rs.10000 each. On selling first, he gains 10% and on theother, he loses 10%. What is profit/loss in the transition?

a) 1%loss b) 1% gain c) 2%loss d) 2% gain e) None

www.OnlineIAS.com



ARITHMETIC58. A shop keeper marks piece of his articles 12% above the cost price and then allows

12% discount on the marked price. What is his loss percent?

a) 0% b) 1% c) 1.44% d) 2.4% e) None

59. On increasing price of an article by 20%, number of articles sold fell by 20%. What iseffect of this on total sales of the article?

a) 4%decrease b) 4%increase c) 20%decrease d) No effect e) None

60. A merchant marks price of his articles 20% above cost price and allows 10% discounton the marked price. What percent profit does he make?

a) 8% b) 10% c) 12% d) 30% e) None

61. A merchant marks price of his articles 25% above the cost price and allows 12%discount to customers. What percent profit does he make?

a) 8% b) 10% c) 13% d) 16% e) None

62. A shopkeeper marks his goods 20% higher than the cost price and sells them at 25%above the marked price. Find his profit percent.

a) 20% b) 25% c) 33 1/3% d) 50% e) None

63. A sells an article to B at a profit of 20%. B sells it to c at a profit of 10%. How manypercent will C pay more than what A pays?

a) 28% b) 30% c) 32% d) 35% e) None

64. Two tables are purchased for the total cost of Rs.5000. First table is sold at 40% profitand second at 40% loss. If selling price is same for both the tables, what is the costprice of the table that was sold at profit?


65. A shopkeeper bought 2 pens for Rs.480. He sold the first at a loss of 15% and thesecond at a profit of 19%. Find cost price of the second pen, if selling price of both thepens are same.


66. A man sold two articles for Rs.600 each. On selling first, he gains 20% and on theother be loses 10%. What is his percent profit in the transaction?

a) 24.8% b) 25% c) 50% d) 56% e) None

www.OnlineIAS.com



ARITHMETIC67. A man sold two articles for Rs.2500 each. On selling first, he gains 20% and on the

other he loses 10%. What is his percent profit in the transaction?

a) 2.18% b) 2.86% c) 5% d) 10% e) None

68. A fruit seller buys oranges @ 3 for Rs.2 and sells them @ 4 for Rs.3. His profitpercent is:

a) 10% b) 12.5% c) 25% d) 50% e) None

69. A fruit seller buys oranges @ 3 for Rs.2 and sells them @ 2 for Rs.3. His profitpercentage is:

a) 125% b) 100% c) 50% d) 25% e) None

70. A fruit seller buys oranges @ 8 for Rs.10 and sells them @ 10 for Rs.8. His profit/losspercentage is:

a) 36%loss b) 36% gain c) 45% gain d) 45% loss e) None

71. A merchant buys oranges at a certain price per dozen and sells them charging 9times that price for 100 oranges. Find his profit percent.

a) 5% b) 8% c) 10% d) 12.5% e) None

72. A fruit seller buys oranges A 3 oranges for Re.1 and sells them @ Rs.3 each. Hispercentage profit is.

a) 50% b) 100% c) 200% d) 800% e) None

73. A retailer bought some apples @ 7 apples for Rs.4 and sold them @ 8 apples forRs.5. If he gains Rs.30 on that day, find the quantity of apples sold by him on thatday.

a) 56 b) 70 c) 80 d) 560 e) None

74. A man bought some oranges as the rate of 3 oranges for one rupee and equalnumber of oranges at the rate of 2 oranges for one rupee. What is his profit, if hesells 2 oranges for one rupee.

a) 20% b) 33.33% c) 50% d) 54.22% e) None

75. A shopkeeper sold one-third of his articles at 16% profit and the remaining at 10%profit. Find his overall profit percent.

a) 12% b) 15% c) 26% d) 36% e) None

www.OnlineIAS.com



ARITHMETIC76. A shopkeeper sold one-third of his articles at 5% profit. At what profit percent should

he sell the remaining articles so that his overall gain is 15%.

a) 10% b) 20% c) 25% d) 30% e) None

77. A shopkeeper sold one-fourth of his articles at 15%loss. At what profit percent shouldhe sell the remaining articles so that his overall gain is 6%?

a) 13% b) 16% c) 17% d) 21% e) None

78. By selling 4 articles, a shopkeeper gains equal to the cost price of 1 article. Find hisgain percent.

a) 10% b) 20% c) 25% d) 30% e) None

79. If the cost price of 11 oranges is equal to selling price of 10 oranges. Find profitpercent.

a) 9% b) 9.99% c) 10% d) 11.11% e) None

80. By selling 10 articles, a shopkeeper gains equal to the selling piece of 2 articles.Find his loss percent.

a) 6.33% b) 20% c) 25% d) 30% e) None

81. On selling 10 articles, a merchant loses equal to cost price of 2 articles. Find hisloss percent.

a) 12.5% b) 20% c) 25% d) 33.33% e) None

82. If the cost price of 15 tables is equal to selling price of 20 tables. Find profit/losspercent.

a) 5%loss b) 5%gain c) 25%gain d) 25%loss e) None

83. By selling 18 articles, a shopkeeper loses the selling price of 2 articles. Find hisloss percent.

a) 10% b) 11.11% c) 12.5% d) 25% e) None

84. A trader marked his goods at 20% above the cost price. He sold half the stock atmarked price, one quarter at a discount of 20% on marked price and rest at adiscount of 40% on the marked price. What is his total gain?

a) 2% b) 3% c) 4% d) 6% e) None

85. A milk seller purchased milk at the rate of Rs.10 per liter and adds one fifth of waterto it. What percent profit does he make by selling the mixture at Rs.12 per liter?

a) 20% b) 25% c) 30% d) 50% e) None

www.OnlineIAS.com



ARITHMETIC86. The profit earned on selling an article for Rs.575 is equal to loss suffered when the

article is sold for Rs.325. find the cost price of the article.

a) Rs.650 b) Rs. 550 c) Rs.500 d) Rs.450 e) None

87. An article is sold for Rs.500 and hence lost some thing. Had the article is sold forRs.700, the merchant would have gained three times the former loss. Find the costprice of the article.

a) Rs. 525 b) Rs.550 c) Rs.600 d) Rs.650 e) None

88. On selling an article for Rs. 270, the amount of loss suffered is as much as profitearned on selling the article at 10% profit. What is the selling price if the desiredprofit is 20%?


89. On selling an article for Rs. 440, the amount of loss suffered I sdouble of profit madeon selling the article at 6% profit. What is the cost of the article?


90. An article is sold for Rs.190, hence gaining a certain amount. Had the article beensold for Rs.175, he would have suffered loss equal to 50% of the gain in the firstcase. Find cost price of the article?


91. If selling price of an article is 4/3 of cost price, then profit percent is:

a) 1/3% b) 25% c) 33.33% d) 50% e) None

92. If cost price of an article is 3/2 of its selling price, the profit or loss percent is:

a) 33.33%loss b) 33.33%profit c) 50%loss d) 50%profit e) None

93. If selling price of 4/5 of the stock of oranges is equal to cost price of the whole stock,find profit percent.

a) 20% b) 25% c) 30% d) 33.33% e) None

94. Find the profit percent made on selling an article for a certain amount, if on slling thearticle for ¾ of the amount causes 10% loss?

a) 2.5% b) 7.5% c) 15% d) 20% e) None

95. A man sold two articles for Rs.990 each. On selling first, he gains 10% and on theother, he loses 10%. Find his total gain or loss>

a) Rs.9.90 b) Rs.10 c) Rs.19.80 d) Rs.20 e) None

www.OnlineIAS.com



ARITHMETIC96. A man sold two articles for Rs.120 each. On selling first, he gains 20% and on the

other, he loses 20%. Find his total gain or loss.

a) Rs.4.80 b) Rs.5 c) Rs.9.60 d) Rs. 10 e) None

97. A shopkeeper buys articles at 20% discount on marked price and sells them at 50%profit. How much percent the selling is above the Marked price?

a) 20% b) 30% c) 60% d) 70% e) None

98. A merchant marks price of his articles 20% above the cost price allows some discounton the marked price and hence makes 8% profit. Find the rate of discount.

a) 10% b) 12% c) 28% d) 30% e) None

99. A merchant marks price of the articles 25% above the cost price and allows somediscount on the marked price and hence makes 8% profit. Find the rate of discount.

a) 10% b) 12% c) 12.5% d) 15% e) None

100. A merchant earns 20% profit, even after allowing 20% discount on the marked priceof an article. How much the marked price is above the cost price ?

1) 40% b) 36% c) 44% d) 50% e) None

101. A merchant makes 60% profit, after allowing 20% discount on the marked price of an article. How much the marked price is above the cost price ?

a) 60% b) 80% c) 92% d) 100% e) None

102. A shopkeeper allows 4% discount on the marked price of an article and earns 20% profit. Find his profit percent, if he allows 10% discount.

a) 12% b) 12.5% c) 14% d) 16% e) None

103. A shopkeeper earns a profit of 25%, after allowing 10% discount on the list price.What is the cost price of an article whose list price is Rs. 500 ?


104. A shopkeeper marks his articles 20% above the cost price and gives a discount of10% on the marked price. Find the cost price of the article, if the selling price isRs.540.


www.OnlineIAS.com



ARITHMETIC105. A profit of 20% is earned even after allowing 4% discount on the marked price. How

much the marked price is above the cost price ?

a) 16% b) 24% c) 25% d) 30% e) None

106. A merchant makes a profit of 12%, after allowing 30% discount on the marked price.How much the marked price is above the cost price ?

a) 42% b) 45% c) 60% d) 80% e) None

107. On allowing 20% discount, 12% loss is suffered. How much the marked price isabove the cost price ?

a) 8% b) 10% c) 12% d) 15% e) None

108. A shopkeeper gains 17% after allowing a discount of 10% on the marked price of anarticle. Find his profit percent if the articles are sold at marked price allowing nodiscount.

a) 23% b) 27% c) 30% d) 37% e) None

109. A man sold one watch and one pen for Rs. 492 and Rs. 168 respectively, gaining10% of the total cost price of the two articles. Had he sold the watch for Rs. 435 andthe pen at its cost price, he would have lost 5% on the total cost price. Find the costprice of the watch.


ANSWERS FOR PROFIT AND LOSS:

1) c 2) d 3) c 4) a 5) b 6) c 7) d 8) c 9) a 10) d 11) b 12) b 13) c 14) b

15) c 16) c 17) a 18) b 19) d 20) d 21) b 22) c 23) c 24) b 25) a 26) b 27) e 28) e

29) d 30) d 31) b 32) b 33) b 34) b 35) c 36) e 37) c 38) c 39) a 40) b 41) c 42) a

43) a 44) a 45) a 46) c 47) b 48) a 49) c 50) c 51) d 52) b 53) c 54) b 55) a 56) d

57) a 58) c 59) a 60) a 61) b 62) d 63) c 64) a 65) b 66) a 67) b 68) b 69) a 70) a

71) b 72) d 73) d 74) a 75) a 76) b 77) a 78) c 79) c 80) c 81) b 82) d 83) a 84) a

85) d 86) d 87) b 88) c 89) c 90) b 91) c 92) a 93) b 94) d 95) d 96) d 97) a 98) a

99) b 100)d 101)d 102)b 103)a 104)b 105)c 106)c 107)b 108)c 109)d

www.OnlineIAS.com



ARITHMETIC

Formula: The average of ‘n’ observations = The total of n observations/n or A=T/n

Whre A = averages; T = total; n = number of things:

Formula: If each observation is incresed by K, then the avrage also incresed by K, then theaverage also increased by L. then the average also decreases by K. If each observation ismultiplied or divided by K, the average is also multiplied or divided by K.

Formula: The average of m things is x ; the average of n thing is y , then the average of m+n

things isnm

ynxm

Formula: The average of m things is x , the average of n things out off the m things is y .

Then the average of remaining things isnm

ynxm

EXERCISE

1. The average of 99 items is 27. If 3 is added to each number of the series, the new average

a) 25 b) 27 c) 30 d) 33 e) None

2. The average of 18 numbers is 24. If each item of the series is multiplied by 3, the newaverage is :

a) 8 b) 24 c) 27 d) 72 e) None

3. The average of first 47 natural numbers is :

a) 23 b) 24 c) 25 d) 47 e) None

4. If the average of five consecutive numbers is 23, find the smallest number.

a) 20 b) 21 c) 22 d) 25 e) None

5. If sum of three consecutive odd numbers is 63, find the first term.

a) 19 b) 21 c) 22 d) 23 e) None

6. Average of first seven multiplies of 7 is :

a) 7 b) 14 c) 28 d) 35 e) None

6. AVERAGE

www.OnlineIAS.com



ARITHMETIC7. Find the average of first eight multiplies of 6.

a) 18 b) 24 c) 27 d) 30 e) None

8. Average of first five odd multiples of 3 is :

a) 12 b) 15 c) 18 d) 21 e) None

9. Out of three numbers, first number is twice of the second and thrice of the third number.If average of the three numbers is 550, what is the smallest number ?

a) 50 b) 100 c) 150 d) 300 e) None

10. If average of 5 observations is 46 and that of 5 other observations is 50, find the averageof all the 10 observations.

a) 96 b) 50 c) 48 d) 46 e) None

11. Average of ‘n’ observations is 35, average ‘n’ other observations is 37 and average ofremaining ‘n’ observations is 42. Average of all the observations is :

a) 36 b) 38 c) 40 d) 57 e) None

12. One year ago, the population of a town was 12000. In one year, male population isincreased by 8% and female population by 6% but the total population is increased by7%. What was the size of the male population one year ago.

a) 5000 b) 5500 c) 6000 d) 7000 e) None

13. Sum of three consecutive even numbers is 32 more than the average of the numbers.Find middle number in the series.

a) 14 b) 16 c) 18 d) 20 e) None

14. The average monthly income of A and B is Rs. 5500, average monthly income of B and Cis Rs. 4500 and the average monthly income of A and C is Rs. 4000. What is the monthlyincome of B ?


15. The average age of 40 students in a class is 15 years. If the age of teacher is alsoincluded, the average becomes 16 years, find the age of the teacher.

a) 15 years b) 16 years c) 55 years d) 56 years e) None

16. The average of 11 numbers is 70 and that of first 10 numbers is 69. The 11th number is :

a) 59 b) 79 c) 80 d) 81 e) None

www.OnlineIAS.com



ARITHMETIC17. The average marks obtained by ten students is 45 and that of eleven students is 48. How

many marks did the eleventh student obtain ?

a) 76 b) 78 c) 80 d) 86 e) None

18. A cricketer has an average of 28 runs in 24 innings. How many runs must he score in the25th inning to make his average 29 ?

a) 1 b) 4 c) 5 d) 53 e) None

19. The average age of 25 students of a class is 13 years. If the age of teacher is alsoincluded, the average age is increased by 2 years. Find the age of the teacher.


20. The average age of 4 brothers is 6 years. If age of their father is included, the average isincreased by 5 years. Find the age of the father.


21. Average age of 6 persons is decreased by 1 year when one new person is included in thegroup. Find the age of new man, if average age of 6 persons was 38 years.


22. Out of 10 terms, the average of first 5 terms is 34 and that of last 5 terms is 38. If theaverage of first 9 items is 35, find the 10th term.

a) 26 2) 35 c) 44 d) 45 e) None

23. The average marks obtained by a group of 10 students is 41 marks. Find the new averageif a new student who scored 63 marks is also included in the group.

a) 39 b) 40 c) 43 d) 45 e) None

24. The average of 9 items is 79. If one new item whose value is 59 is also included in theseries, find average of all the 10 items.

a) 77 b) 80 c) 81 d) 83 e) None

25. Average age of 9 members of a club is 29 years. If 2 more persons with the average ageof 40 years have become the members of the club, find average age of all the 11 members.


26. A batsman has a certain average of runs for 16 innings. In the 17th inning, he scores 85runs, thereby increases his average by 3 runs. What was his average before 17th inning ?

a) 88 runs b) 82 runs c) 34 runs d) 37 runs e) None

www.OnlineIAS.com



ARITHMETIC27. The batting average of a cricketer for 78 innings is 38 runs. His highest score exceeds

the lowest score by 226 runs. If these two innings are excluded, the average of theremaining innings is 36 runs. What is his highest score ?


28. Average age of 6 sons of a family is 8 years. Average age of sons together with theirparents is 22 years. If father is older than mother by 8 years, the age of mother is :


29. Average age of 12 men is increased by 2 years when one man whose age is 43 years isreplaced by a new man. Find the age of the new man.


30. Average age of 18 men is decreased by 1 year when one man whose age is 49 years isreplaced by a new man. Find age of the new man.


31. The average weight of 12 persons is 50 kg. On replacing a man whose weight is 53 kg.with a new man, new average becomes 49 kg. The weight of the new man is :

a) 41 kg b) 46 kg c) 54 kg d) 65 kg e) None

32. On replacing an old member of a group with a young member, the average age of 10members of the group remains same as it was 2 years ago. How much is the newmember younger than the old one ?


33. Average age of 6 persons in a group is same as it was 5 years ago, when an old man inthe group is replaced by a young man, what is the age of the new person if the manreplaced is of 70 years.


34. Average weight of 30 students in a class is increased by 200 grams when one studentwhose weight is 20 kg. is replaced by a new student. Find the weight of the new studentadmitted.


35. The average age of 12 men in a group increased by 2 years when two men whose agesare 20 years and 22 years, are replaced by new members. What is the average age of thenew men included ?


www.OnlineIAS.com



ARITHMETIC36. The average marks obtained by 9 students were calculated to be 65. Later on it was

found that the marks of one student was wrongly read as 76 instead of 67. The correctaverage is :

a) 56 b) 64 c) 66 d) 74 e) None

37. Average marks of 100 students is 58. Later on it is found that marks of one student ismisread as 47 instead of 87. Find the correct average.

a) 57.4 b) 57.6 c) 58.4 d) 58.6 e) None

38. Average age of 15 men is increased by 1 year when one man in the group is replaced withother man whose age is 49 years. Find the age of the man replaced.


39. Four years ago, the average age of 4 persons A, B, C and D was 38 years. With joiningof E, now the average age of 5 persons becomes 36 years. Find E’s present age.


40. Average age of 7 members of a family is 29 years. If present age of the youngest membersis 5years, find average age of the remaining members at that time of birth of the youngestmember.


41. Average weight of 8 persons is 48 kg. If one man weighing 34 kg. is dies, what is averageage of the remaining 7 persons.


42. Average runs scored by 11 players of a cricket team is 23 runs. If the first player scored113 runs. Find the average of the remaining players.


43. Average weight of 20 boys and 15 girls in a class is 29 kg and 22 kg respectively. Find theaverage weight of all the students in the class.


44. The average expenditure of a man for 10 days is Rs. 45 per day. If his average expenditurefor the first 3 days is Rs. 52 per day, find his average expenditure for the remaining 7days.


www.OnlineIAS.com



ARITHMETIC45. Average age of 12 persons in a group is 25 years. On including 3 more persons in the

group, the average age is decreased by 1 year. Find the average age of the three newmembers.


46. The average weight of the students of a class is 40kg. 5 new students with the averageweight of 46 kg. having joined the class, the average weight of the class is increased by2kg. Find the number of students in the class originally ?

a) 10 b) 15 c) 20 d) 25 e) None

47. 4 years ago, the average age of 5 members of a family was 22 years, A baby having beenborn, the average age of the family is the same today. Find the age of the baby.


48. Average marks obtained by first 10 students out of 11 students in a class is 189. If thefirst student has obtained 163 marks and the 11th student 193 marks, find the averagemarks of the last 10 students.

a) 190 b) 192 c) 199 d) 219 e) None

49. Average temperature for Monday, Tuesday and Wednesday is 350C and that for Tuesday,Wednesday and Thursday is 360C. What is the temperature on Thursday, if temperatureon Monday is 310C ?

a) 310C b) 340C c) 350C d) 360C e) None

50. Average temperature 9th to 16th of a month is 300C and that from 10th to 17th 310C. What isthe temperature on 17th, if temperature on 9th is 350C ?

a) 290C b) 260C c) 320C d) 430C e) None

51. Average temperature from Monday to Saturday is 390C and that from Tuesday to Sundayis 370C. What is the temperature on Monday, if temperature on Sunday is 320C?

a) 200C b) 260C c) 380C d) 440C e) None

52. The average temperature from Monday to Friday is 380C and that from Tuesday to Saturdayis 350C. Find temperature on Monday, if ratio between the temperatures on Monday andSaturday is 8:5 ?

a) 250C b) 370C c) 400C d) 440C e) None

53. On replacing 2 men weighing 45 kg. and 31 kg. with two new members, the averageweight of 10 men in a group is increased by 3kg. Find the average weight of two newmembers.


www.OnlineIAS.com



ARITHMETIC54. The average of 11 observations is 72. If average of first 5 observations is 70 and that of last

5 observations is 71, then the 6th observation is :

a) 72 b) 75 c) 82 d) 87 e) None

55. The average of 9 numbers is 25. The average of first 5 numbers is 22 and that of last 3numbers is 27. Find the 6th number.

a) 16 b) 24 c) 26 d) 34 e) None

56. The average of 10 numbers is 16. If average of first 6numbers is 17 and that of last 3numbers is 13. Find the 7th number.

a) 13 b) 14 c) 19 d) 21 e) None

57. The average marks obtained by 24 students of a class is 64. If the average marks of thefirst 6 students is 72 and that of the next 17 students is 62, find the marks obtained bythe last students.

a) 50 b) 58 c) 67 d) 78 e) None

58. The average of 11 observations is 50. If average of first 6 observations is 49 and that of last6 observations is 52, then the 6th observation is :

a) 44 b) 56 c) 64 d) 70 e) None

59. The average of 15 numbers is 8. If average of first 8 members is 10 and that of last 8numbers is 9, find the 8th number.

a) 8 b) 16 c) 24 d) 24 e) 32

60. The average of 11 observations is 72. If average of first 6 observations is 70 and that of last6 observations is 71, then the 6th observation is :

a) 54 b) 75 c) 78 d) 87 e) None

61. The average of 9 readings is 9. The average of first 5 readings is 10 and that of last 5readings is 8. What is the 5th reading ?

a) 9 b) 10 c) 9.5 d) 8 e) None

62. Average age of 13 students of a class is 12 years. If average age of first four students is11 years and that of last 10 students is 13 years, what is the age of fourth student ?


63. The average expenditure of 40 persons is Rs. 60 per day and that of 60 other persons isRs. 40 per day. Find the average expenditure of all the 100 persons.


www.OnlineIAS.com



ARITHMETIC64. The average age of 30 persons is 20 years and that of 20 other persons is 30 years. Find

the average age of all the 50 persons.


65. Average students from class I to X in a school is 54. What is the average number ofstudents in class I to III, if the average number of students in the remaining seven classesis 57 ?

a) 47 b) 50 c) 51 d) 60 e) None

66. Average expenditure of a person for the first 3 days of a week is Rs. 350 and for the next4 days is Rs. 420. Average expenditure of the man for the whole week is ?


67. Average expenditure of a person for the first 5 months of a year is Rs. 2500 per monthand that for the next 7 months is Rs. 2740. Average expenditure of the man for the yearis :


68. A man’s average expenditure for first 11 days of a month was Rs. 104 per day and for thenext 19 days, it was Rs. 98 per day. If he could save RS. 54 during that month, find hisincome for the month ?


69. A shopkeeper purchased 25 kg. of sugar at Rs. 5 per kg. and 75 kg. of sugar Rs. 9 perkg. He mixed the two varieties and sells the mixture at Rs. 10 per kg. find his profitpercentage.

a) 11.11% b) 25% c) 33.33% d) 100% e) None

70. The batting average of a batsman in 42 innings is 45 runs. He was out for a duck in 7innings. His batting average for the remaining innings is :

a) 50 b) 54 c) 55 d) 60.25 e) None

71. The batting average of a batsman in 57innings is 58 runs. He was out for a duck in 7innings. His batting average for the remaining innings is :

a) 60 b) 65 c) 66.12 d) 70.28 e) None

72. 11 friends went to a hotel and decided to pay the bill amount equally. But 10 of themcould pay Rs. 60 each as a result 11th has to pay Rs. 50 extra than his share. Find theamount paid by him.


www.OnlineIAS.com



ARITHMETIC73. 9 men started a partnership business contributing Rs. 10000 each. Later on 10th men

joined the partnership contributing Rs. 3600 more than the average contribution of all the10 men. How much did the 10th men contribute.


74. 5 men started a business contributing Rs. 20000 each. Later on 6th men joined thepartnership contributing Rs.2000 less that the average contribution of all the 6 men. Findthe amount contributed by the 6th partner.


75. The average marks obtained by some students in an examination is 54. If 20% of thestudents got a mean score of 90 marks and the 30% of the students got a mean score of20. Find the average marks of the remaining students.

a) 42 b) 45 c) 50 d) 600 e) None

ANSWERS FOR AVERAGEEXERCISE

1) c 2) d 3) b 4) b 5) a 6) c 7) c 8) b 9) d 10) c 11) b 12) c 13) b 14) c

15) d 16) c 17) b 18) d 19) a 20) b 21) 22) c 23) a 24) b 25) c 26) c 27) c 28) c

29) d 30) a 31) a 32) d 33) c 34) c 35) b 36) b 37) c 38) a 39) b 40) d 41) b 42) c

43) c 44) b 45) b 46) a 47) a 48) b 49) b 50) d 51) d 52) c 53) c 54) d 55) d 56) c

57) a 58) b 59) d 60) a 61) a 62) b 63) b 64) a 65) a 66) b 67) c 68) c 69) b 70) b

71) c 72) c 73) c 74) b 75) d

www.OnlineIAS.com



ARITHMETIC

Rule of Allegation given us the ratio in which two quantities, one at price and anotherlower price, should be mixed to produce a mixture given price. This rule can be applicable incase of solutions of hence strengths also.

Cost of higher price is Rs. x, the last of lower price is Rs.y, these varieties are mixed incertain ratio to give another variety of price.

Then those two varieties should be mixed in the ratio z-y; x-z following figure explains thesame.

Higher price lower price x y

z-y x-zEXERCISE

1. In what ratio two varieties of milk costing Rs.8 and Rs.9 per liter respectively mixed, sothat the mixture costs s. 8.30 per liter

a) 9:8 b) 7:3 c) 3:7 d) 8:9 e) None

2. Two mixtures of milk and water contain 10% and 20% water. In what ratio two mixturesshould be mixed so that the resulting mixture contains 16% water?

a) 1:2 b) 2:1 c) 2:3 d) 3:2 e) None

3. The average weight of 30 students of a class is 45kg.The average weight of girls is37kg.and that of boys is 49kg. Find the number of boys in the class.

a) 10 b) 15 c) 20 d) 22 e) None

4. A merchant sells 50kg.of a commodity – partly at 10% profit and the rest at 15% profit. Ifnet profit in the deal is 13%, then the quantity sold at 10% profit is:


5. A merchant mixes two varieties of wine containing 25% and 13% alcohol. Find the quantityof second mixture, if 8 litres of first mixture is taken.

a) 4 litres b) 16 liters c) 24 liters d) 32 liters e) None

6. The average of students of a class is 11 years. If the average age of boys is 11.2 yearsand that of girls is 10.9 years. Find number of total students, if there are 50 boys in theclass.

a) 100 b) 150 c) 160 d) 200 e) None

7. A merchant sold 80 dozen oranges. He sold some at 4% loss and rest at the cost priceand thus losing 3% on the whole. What is the quantity sold at loss?

a) 20dozen b) 40 dozen c) 50 dozen d) 60 dozen e) None

7. ALLIGATION

z

www.OnlineIAS.com



ARITHMETIC8. A shopkeeper sold 45kg. of goods. If he sells some quantity at a loss of 3% and rest at

17% profit, making 5% profit on the whole, find the quantity sold at profit.


9. A shopkeeper sold 40kg. of goods – partly at 7% profit and rest at 5% loss, suffering 2%loss on the whole, what is the quantity sold at profit ?


10. A mixture of 70liters of wine and water contains 10% water. How much more water shouldbe added to the mixture to make 37% water in the resulting mixture?

a) 37lts b) 30lts c) 27lts d) 18.9lts e) None

11. A mixture of 70 litres of wine and water contains 10% water. How much water should beadded to make 25% water in the resulting mixture?

a) 7lts b) 10.5lts c) 14lts d) 21lts e) None

12. The average for labor in a factory is Rs. 1125 and the v\average salary of 12 officers is3175. Find the total number of employees working in the factory if average salary peremployees is Rs.1330.

a) 30 b) 60 c) 108 d) 120 e) None

13. A man purchased a horse and a cow for Rs.5000. He sells the horse at 20% profit and thecow at 10%loss. If he gains 2% on the whole transaction, the cost of the horse is:


14. In examination, a student gets 3 marks for every correct answer and 1 mark for everywrong answer. If he scores ‘0’ marks in a paper of 100 questions, how many of hisanswers were correct?

a) 25 b) 50 c) 60 d) 75 e) None

15. In an examination, a student gets 3 marks for every correct answer and loses 1 mark forevery wrong answer. If he scores 120 marks in a paper of 100 question, how many of hisanswer were correct?

a) 15 b) 40 c) 55 d) 60 e) None

16. Pure milk costs Rs.10per liter. A milk man adds some water to 20 liters of pure milk andsells the mixture at Rs.8 per liter and hence making no profit or loss. How many liter ofwater does he add?

a) 2 liters b) 5liters c) 8 liters d) 10 liters e) None

17. In what ratio a shopkeeper must add water to milk so that he gains 25% on selling it atcost price?

a) 2:3 b) 3:2 c) 3:1 d) 4:1 e) None

www.OnlineIAS.com



ARITHMETIC18. Pure milk costs Rs.12 per liter . A milkman adds some water to 16 liters of pure milk

and sells the mixture at Rs.10 per liter making 25% profit. How many liters of water doeshe add?

a) 5 liters b) 6 liters c) 8 liters d) 10 liters e) None

19. A shopkeeper mixes two varieties of rice purchased @ Rs.35 per kg and @ Rs.28 per kgrespectively. If he sells the mixture @Rs.36per kg. and thus gains 20%, find the ratio inwhich the two varieties are mixed.

a) 1:1 b) 1:2 c) 5:2 d) 7:4 e) None

20. Two Vessels A and B contain milk and water in the ratio 7:1 and 9:7 respectively. Find theratio in which the mixtures must be taken fro the two Vessels to make the resultantmixture in the ration 2:1

a) 1:1 b) 1:2 c) 5:2 d) 7:4 e) None

21. A batsman has batting average of 27 runs per inning. In the next series of 3 innings hescores only 27 runs, thereby decreases his batting average by 2 runs. Find the totalnumber of innings played by him.

a) 25 b) 50 c) 60 d) 75 e) 27

22. The batting average of a cricket players is 72 runs per innings. In the net 4 innings, hecould score only 80 runs and thereby decreases his batting average by 2 runs. What istotal number of innings played by him till last match ?

a) 125 b) 130 c) 160 d) 100 e) 104

23. The batting average of a cricketer is 50 runs per inning. In the next 5 innings, he scores400 runs and thereby increases his batting average by 5 runs. What is total number ofinnings played by him till last match?

a) 30 b) 60 c) 108 d) 120 e) None

24. A mixture contains milk and water in ratio 4:1. When 10 litres of mixture is replaced withwater, the ratio becomes 2:3. Find the quantity of mixture.

a) 20 b) 30 c) 8 d) 10 e) None

25. A mixture 40 litres contains milk and water in the ratio 4:1. How many litres of mixturemust be replaced with water so that the new ratio is 1:1?

a) 5 liters b) 6 liters c) 8 liters d) 10 liters e) 15 liters

26. A class of 60 students contributed Rs. 4800 for a charity. If each boy has contributed Rs.94 and each girl contributed Rs. 73. Find the number of boys in the class.

a) 25 b) 20 c)28 d) 40 e) NoneANSWERS FOR ALLIGATION

EXERCISE1) b 2) c 3) c 4) a 5) b 6) b 7) d 8) c 9) a 10) b 11) c 12) d 13) a 14) c15) c 16) b 17) d 18) c 19) a 20) b 21) c 22) d 23) b 24) a 25) b 26) a

www.OnlineIAS.com



ARITHMETIC

If a man borrows some money from any other body, he has to pay some extra moneyin addition to the sum borrowed to the lender. That extra money is called interest. If theinterest is calculated uniformly through out the period, the method is called simple interestmethod. The money barrowed is called ‘Principal’, the amount at the end of the 1 periodpayable including interest is called ‘Amount generally rate of interest is expressed as apercent per annum.

According to this method, the simple interest payable at R%, p.a. for a period of T years,

on the principal is100

PTR

Simple interest (I) =100

PTR

AndA = P+I

A = P +100

PTR

A =

1001

TRP

P =TR

A

100

100

Formula: If the sums P1, P2, P3, yield some interest in N1, N2 and N3 years at R1, R2, R3,

rates of interests then P1:P2: P3 =332211

1:

1:

1

RNRNRN and P1:P2 = N2R2:N1R1

Formula: If a sum becomes ‘n’ times in T years at R% p.a. then 100(n-1) = TR (or)T=100(n-1)/R

And R =T

n )1(100

8. SIMPLE INTEREST

www.OnlineIAS.com



ARITHMETICIf the sum of doubles, then n=2

Formula: If a sum becomes m times in ‘y’ years, then it takes to become n times n y2

years then 1

1

2

1

n

m

y

y years.

Simple interest in calculated on the Principal uniformly for each year. In other words,Principal remains same throughout the period.

Principal : The money borrowed by the borrower from the lender is called Principal.

Rate of Interest: Rate at which the principal is charged.

Time : The period at the expiry of which the amount is to be returned.

Amount :The money returned by the borrower at the end of the certain period is calledAmount.

Amount = Principal + Interest

Interest: The extra money paid by the borrower to the borrower to the lender is calledinterest.

Interest = Amount – Principal

Formulae:

1. Simple interest =Principal Rate Time

100

2. Principal =SimpleInterest

Rate Time100

3. Rate of Interest =SimpleInterest

Principal Time100

4. Time=SimpleInterest

Principal Rate100

5. If rate of Simple interest differs from year to year, then

Simple interest = Principal 1 2 3R +R +R +............100

www.OnlineIAS.com



ARITHMETIC

6. Amount = Principal100+(Rate Time)

100

7. Principal = Principal100

100+(Rate Time)

8. If a sum of money becomes double in ‘n’ years. It will become 3 times in ‘2n’

years and fourfold in ‘3n’ years.EXERCISE

1. Simple interest on Rs. 5000 at 10% per annum for 4 year is:a) Rs.1500 b) Rs.2000 c) Rs.2500 d) Rs.5000 e) None

2. Find simple interest on Rs. 1500 for 2 years at eh rate of 1 paise per rupee permonth.a) Rs.30 b) Rs.36 c) Rs. 300 d) Rs.360 e) None

3. Find simple interest on Rs.2000 at 5% p.a. for 2 ½ years.a) Rs.200 b) Rs.250 c) Rs.300 d) Rs.350 e) None

4. Find simple interest on Rs. 7300 for 37 days at 10% p.a.a) Rs.74 b) Rs.370 c) Rs.500 d) Rs.730 e) None

5. Find smile interest on Rs.500 for 3 years, if rate of interest for 3 years is 4% and &%respectively.a) Rs.60 b) Rs.85 c) Rs.90 d) Rs.170 e) None

6. If simple interest on a certain sum at 4% per annum for 4 years is Rs.80, the sum is:a) Rs.320 b) Rs.400 c) Rs.500 d) Rs.600 e) None

7. In now many years will Rs.5000 amount to Rs.6500 at 10% p.a. simple interest?a) 2 years b) 2 ½ years c) 3 years d) 3 ½ years e) None

8. Rs.600 amounts to Rs. 735 in 5 years at a certain rate of simple interest. If the rateof interest is increased by 2%, what will be the amount then?a) Rs.660 b) Rs.700 c) Rs.750 d) Rs.795 e) None

9. A sum of Rs.500 becomes Rs.600 in 2 years at certain rate of interest. What will beamount if the rate of interest is increased by 3%?a) Rs.630 b) Rs.620 c) Rs.570 d) Rs.530 e) None

10. A sum of money is invested for 3 years at a certain rate of simple interest. Had therate of interest been 1% more; it would have fetched Rs.18 more than before. Findthe sum investeda) Rs.540 b) Rs.600 c) Rs.900 d) Rs.1800 e) None

11. The simple interest on a certain sum at 6.5% per annum for 3 years is Rs.123.50.what will be additional interest in the amount was lent at 7% p.a.?a) Rs.4.25 b) Rs.6.75 c) Rs.9.50 d) Rs. 19 e) None

12. Simple interest on Rs.3500 at 10% p.a. for a certain period is Rs.400 more than theinterest on Rs.2500 at 10% p.a. for the same period. Find the time.a) 2 years b) 3 years c) 4 years d) 5 years e) None

13. At what rate per cent of simple interest per annum will a sum of money double itselfin 8 years?a) 8% b) 10% c) 12.5% d) 15% e) None

www.OnlineIAS.com



ARITHMETIC

14. At what rate percent of simple of simple interest per annum will a sum of moneybecome three times in 10 years?a) 5% b) 10% c) 20% d) 25% e) None

15. If difference between simple interest on a certain a sum at 4% for 6 years and at 5%for 4 years is Rs.28, find the sum.a) Rs.200 b) Rs.400 c) Rs.500 d) Rs.700 e) None

16. At what rate percent of simple interest per annum will a sum of money earn interestequal to 3/5 of the principle in 4 years?a) 15% b) 20% c) 25% d) 12.5% e) None

17. A certain sum of money at a certain rate of simple interest becomes double in 10years. It will become three times in:a) 20 years b) 15 years c) 10 years d) 7 ½ years e) None

18. A certain sum of money at a certain rate of simple interest becomes double in 5years. It will become four times in:a) 7 ½ years b) 10 years c) 15 years d) 20 years e) None

19. A man borrowed Rs.700 for 3 years at a certain rate of interest and Rs.400 for 5years at the same rate of interest. If he pays total interest of Rs.246 for both theloans, find the rate of interest.a) 3% b) 4% c) 6% d) 8% e) None

20. A man borrowed Rs.2500 at 4%p.a.and Rs.1800 at 5% simple interest for the sameperiod. If he pays Rs.570 as total interest, find the time for which the sums wereborrowed.a) 2 years b) 3 years c) 4 years d) 5 years e) None

21. At what rate percent of simple interest per annum, Rs.500 lent for 7 years will earnsame interest as Rs.700 earns in 6 years at 10% p.a.?a) 15% b) 20% c) 25% d) 12% e) None

22. In how many years a sum of Rs.2500 at 18% simple interest per annum will earnsame interest as Rs.1500 earns at 10% p.a. in 12 years?a) 3 years b) 4 years c) 5 years d) 6 years e) None

23. If simple interest on Rs.300 for 4 years at certain rate of interest is Rs.100. What willbe the interest on Rs.600 for 8 years at the same rate of interest?a) Rs.400 b) Rs. 200 c) Rs.50 d) Rs. 25 e) None

24. What sum of money lent at 4%p.a. for 3 years will earn same interest as Rs. 1200earns in 4 years at 5%p.a. of simple interest?a) Rs.1000 b) Rs. 1500 c) Rs. 2000 d) Rs. 2500 e) None

25. If a sum of Rs. 500 amounts to Rs.575 in 3 years. How much will Rs. 600 amount toin 4 years at the same rate of simple interest?a) Rs.120 b) Rs. 620 c) Rs. 650 d) Rs. 720 e) None

26. A sum of Rs. 29000 is divided into two parts and invested at simple interest in sucha way that first part invested at 5% p.a. for 6 years earns the same interest as thesecond part for 7 years @ 4%p.a. Find the amount invested in first part.a) Rs. 14000 b) Rs.14500 c) Rs.15000 d) Rs. 16500 e) None

www.OnlineIAS.com



ARITHMETIC

27. A man invested Rs.4000 into two parts at simple interest-one at 4% and other at5%p.a. If interest on first part for 5 years is equal to interest on second part for 6years, find amount invested at 4%.a) Rs.1600 b) Rs.1800 c) Rs. 2000 d) Rs.2400 e) None

28. A main invested Rs. 600 into three parts at simple interest-first part at 3% for 4years, second part at 4% for 5 years and the third part at 5% for 3 years. If interestreceived on each part is equal, find amount invested at 5%.a) Rs. 150 b) Rs. 200 c) Rs. 250 d) Rs. 300 e) None

29. A sum of Rs. 5500 is divided into two parts and invested at 4%p.a.for 3 years and at5%p.a. for 6years respectively. If interest earned on the second part is three times ofthat on the first part, find the amount invested in second part.a) Rs. 2000 b) Rs. 2250 c) Rs. 2500 d) Rs. 3000 e) None

30. A man invested a total sum of Rs.8500 in names of his sons at 4% and 5% respectivelyin such a way that they get equal amount on attaining age of 20 years. If theirpresent ages are 15 years and 13 years respectively, what is the sum invested in thename of elder son?a) Rs. 3750 b) Rs. 4000 c) Rs. 4250 d) Rs. 4500 e) None

31. Rs. 4310 is invested into three parts at simple interest so that the amounts receivedafter 1,2 and 3 years respectively in each part are equal. Find the amount investedfor 3 years, if rate of interest is 10%p.a.a) Rs. 1320 b) Rs. 1430 c) Rs. 1560 d) Rs. 1650 e) None

32. What sum will amount to Rs. 660 in 4 years 8%p.a. of simple interest?a) Rs. 500 b) Rs. 550 c) Rs. 600 d) Rs. 650 e) None

33. What sum will amount to Rs. 2300 in 3 years at simple interest of 5% p.a.?a) Rs. 1800 b) Rs. 2000 c) Rs. 2100 d) Rs. 2500 e) None

34. A sum amounts to Rs. 5750 in 3 years at 5%p.a. simple interest. In how many yearswill the sum amount to Rs. 7000 at the same rate of interest?a) Rs. 1500 b) Rs. 1600 c) Rs. 1700 d) Rs. 1800 e) None

35. A sum of money amounts to Rs. 1800 in 3 years and Rs. 2000 in 5 years at simpleinterest. Find the Principal.a) Rs. 1500 b) Rs. 1600 c) Rs. 1700 d) Rs. 1800 e) None

36. A certain sum of money amounts to Rs. 600 in 2 years and Rs. 700 in 4 years at acertain rate of simple interest. Find the rate of interest.a) 5% b) 8.16% c) 10% d) 16.33% e) None

37. If simple interest on a certain sum is ¼th of the principal and the numbers of years areequal to the rate percent annum, the rate of interest per annum is:a) 5% b) 10% c) 20% d) 25% e) None

38. If simple interest on a certain sum of money is 1/9th of the principal and the numbersof years are equal to the rate percent per annum, the rate of interest per annum is:a) 3% b) 1/3% c) 10/3% d) 3/10% e) None

39. A man invested1/3 of his income at5% p.a1/4th of the income at 4% and the remaining5/12 income at 3%. If his annual income is Rs. 470, find the money invested by him.a) Rs. 3000 b) Rs. 6000 c) Rs. 12000 d) Rs. 15000 e) None

www.OnlineIAS.com



ARITHMETIC40. A man lent Rs. 2000 – partly at 5% and the balance at 4%. If he receives Rs. 92

towards annual interest, find the amount lent at 5%.a) Rs. 1200 b) Rs. 1600 c) Rs. 1204 d) Rs. 1500 e) None

41. A man inverted Rs. 3500 into two parts at Simple interest – one at 4% and other at6% p.a. If his yearly income from investment is Rs. 170, how much did he invest at6%?a) Rs. 300 b) Rs. 600 c) Rs. 1200 d) Rs. 1500 e) None

42. A person lent a sum of money @ 6% p.a. In 8 Years, the Simple interest was Rs. 260less than the sum lent. Find out the sum lent.a) Rs. 400 b) Rs. 600 c) Rs. 800 d) Rs. 500 e) None

43. Two equal sums of money are deposited in different banks – first parts at 5% p.a.simple interest for 4 years and second part at 4% p.a. Simple interest for 6 years. Ifdifference between the two interests is Rs. 100, find the sum deposited in eachbank.a) Rs. 2500 b) Rs. 6000 c) Rs. 12000 d) Rs. 5000 e) None

44. Find the amount of equal installment, annual payment of which will discharge a debtof Rs. 848 due in 4 years at 4% p.a. of Simple Interest.a) Rs. 1320 b) Rs. 1430 c) Rs. 1560 d) Rs. 1650 e) Rs. 200

45. Find the amount of debt that will be discharged by 5 equal installments of Rs. 200each, if the debt is due in 5 years 5% p.a.a) Rs. 1120 b) Rs. 1430 c) Rs. 1160 d) Rs. 1150 e) Rs 1100

ANSWERS FOR SIMPLE INTERESTEXERCISE

1) b 2) d 3) b 4) a 5) b 6) c 7) c 8) d 9) a 10) b 11) c 12) c 13) c 14) c

15) d 16) a 17) a 18) c 19) c 20) b 21) d 22) b 23) a 24) c 25) d 26) a 27) d 28) b

29) d 30) d 31) a 32) a 33) b 34) c 35) a 36) c 37) a 38) c 39) c 40) a 41) d 42) d

43) a 44) e 45) e

www.OnlineIAS.com



ARITHMETIC

In an compound method interest is calculated on the interest again. If the borrower doesnot pay the interest every year to the lender, the lender considers the unpaid interest as sumgiven and calculates interest on this accrued interest also. Hence for more than one yearperiod, the compound interest receivable will be more than the simple interest for the sameperiod at the same rate.

The interest may be calculated quarterly, half-yearly or annually. Generally it is annuallycalculated. If the interest is calculated half-yearly or quarterly the rate of interest should alsobe reduced to that period.

In the working of problems, consider amount = A, sum given = P; no. of times the interestis calculated = n ; the rate of interest for the period of calculation of interest = r.

Formula: 1. Interest calculated annually at the end of n years : A=n

rp

1001

2. Interest calculated half-yearly, no.of times interest is calculated = n, then A =n

rp

2

2001

3. R a t e o f i n t e r e s t f o r 1

st year r%, for 2nd year r2% and so on, then A =nn

rrp

221

2001

1001

4. If the total period of time is n years and y th part of a year (like 2 years a months = 212

9

years or 2 ¾ years) then A =

1001

1001

ryrp

n

, hence for 2 years a months period

A=

400

31

1001

2rr

p

5. If a sum Rs. Z is due after n years and is payable in n annual equal installments then

zxrr

xznn

.....100

1100

11

Where ‘x’ is the annual installments.

6. If recent worth of a sum Rs. Z due after n years at this method isn

r

z

2001

9. COMPOUND INTEREST

www.OnlineIAS.com



ARITHMETICIn each of compound interest, amount for the first year becomes the principal for the secondyears, amount for the second year becomes the principal for the third years and so on.

Compound interest = PrincipalTimeRate1+

100

Principal

If interest is compounded half-yearly, rate of interest is halved i.e. rate becomes r/2 and timeis doubled i.e. time becomes 2t and if interest is compounded quarterly, rate of interest isdivided by 4 i.e. rate becomes r/4 and time is multiplied by 4 i.e. time becomes 4t and so on.It is recommended to convert r% into fraction for solving problems on compound interest.

Time

Time

Time

RateAmount =Principal 1+100

AmountPrincipal=Rate1+100

Amount Rate3. = 1+Principal 100

1.

2.

EXERCISE1. Find compound interest on Rs. 1600 at 2.5% p.a. for 2 years

a) Rs. 80 b) Rs. 81 c) Rs. 82 d) Rs. 108 e) Rs 110

2. Find compound interest on Rs. 8000 at 5% p.a. for 3 years


3. Rs. 10000 is borrowed at 20% p.a., interest compounded half-yearly. Find the amountrepayable after one year.


4. Find compound interest on Rs. 8000 at 20% p.a. for 9 months, interest being compoundedquarterly.


5. Find compound interest on Rs. 25000 at 20% p.a. for 2 ½ years, if interest is compoundedannually.


6. Find compound interest on Rs. 10000 at 10% p.a. for 4 years, if interest is compoundedannually.


www.OnlineIAS.com



ARITHMETIC7. Find Compound interest on Rs. 10000 for 3 years if rate of interest is 5%, 10% and 20%

for first, second and third years respectively.


8. If compound interest for second year on a certain sum at 10% p.a. is Rs. 132, find theprincipal.


9. If compound interest on a certain sum for 2 years at 10% p.a.is Rs.315,what is the sumlent?


10. A certain sum of money inverted at a certain rate of compound interest doubles in 5years. In how many years will it become 4 times?

a) Rs. 12 years b) Rs. 21 years c) Rs. 25 years d) Rs. 31 years e) Rs 10 years

11. A certain sum of money invested at a certain rate of compound interest doubles in 6years, In how many years will it become 8 times?


12. An amount is lent at 15% p.a. compound interest for 2 years. Find the percent increasein the amount at the end of 2 years.

a) 3% b) 1/3% c) 10/3% d) 3/10% e) 32.25%

13. A person returns Rs. 1331 years after 3 years from the date of borrowing. If the arte ofinterest is 10% p.a., interest compounded annually, find the amount borrowed.


14. In how many years will Rs. 400 amount to Rs. 441 at 5% compound interest?


15. The population of a village increases @ 5% p.a. If present population is 8000, after howmany years the population will be 9261?


16. If Rs. 8000 amounts to Rs. 8820 in 2 years at compound interest, find rate of interest p.a.

a) 5% b) 10% c) 20% d) 25% e) None

www.OnlineIAS.com



ARITHMETIC17. At what rate percent of compound interest will a sum be 16 times of itself in 4 years?

a) 100% b) 110% c) 50% d) 25% e) None

18. At what rate percent of compound interest, a sum of Rs. 2000 will amount to Rs. 2662 in3 years?

a) 5% b) 10% c) 20% d) 25% e) None

19. A man invested Rs. 16000 at compound interest for 3 years, interest compounded annually.If he got Rs. 18522 at the end of 3 years, what is rate of interest?

a) 5% b) 10% c) 20% d) 25% e) None

20. Height of a tree is 1210cm. What was its height two years ago, if it increases at the rateof 10% p.a.?

a) 1200 cm b) 1500 cm c) 1000 cm d) 1150 cm e) 12010 cm

21. Cost of a machine is Rs. 10000 and it depreciates 20% annually. Its value two yearshence will be:


22. The value of a machine depreciates @ 25% p.a. If its present value is Rs. 14400, whatwill be its worth after 2 years.


23. The value of a machine depreciates @ 25% p.a. If its present value is Rs. 1400. Find thevalue of machine 2 years ago.


24. If a certain sum on compound interest becomes Rs. 2000 in 2 years and Rs. 2200 in 3years, find rate of interest p.a.

a) 5% b) 10% c) 20% d) 25% e) None

25. Compound interest on a certain sum for two successive years in Rs. 150 and Rs. 153respectively. Find rate of interest.

a) 2% b) 6% c) 5% d) 8% e) None

26. If a certain sum on compound interest becomes Rs. 2000 in 2 years and Rs. 2420 in 4years. Rate of interest p.a. is:

a) 5% b) 10% c) 20% d) 25% e) None

www.OnlineIAS.com



ARITHMETIC27. A certain sum of money amounts to Rs. 640 after 2 years and Rs. 720 after 3 years. How

much will it amount to in 4 years?


28. A sum of money amounts to Rs. 2880 in 2 years and 3456 in 3 years at compoundinterest. Find the sum.


29. Find the rate percent of compound interest at which a sum of money will amount to 9/4times of itself in 2 years?

a) 5% b) 10% c) 20% d) 25% e) 50%

30. Find the rate percent of compound interest a t which a sum of money will become 1.44times itself in 2 years?

a) 5% b) 10% c) 20% d) 25% e) None

31. A man borrow Rs. 2100 and undertaken to pay back with compound interest @ 10% p.a.in 2 equal yearly installments at the end of first and second year, What is the amount ofeach installment?


32. A man borrow Rs. 820 and undertakes to pay back with compound interest @ 5%p.a. in2 equal yearly installments at the end of first and second year. What is the amount ofeach installment?


33. A man borrows Rs. 1820 and undertakes to pay back with compound interest @ 20%p.a.in 3 equal yearly installments at the end of first, second and third years, What is theamount of each installment?


34. A man borrows a certain sum and pays it back in two equal annual installments. If he payback Rs. 676 annually and rate of interest is 4%, what is the sum borrowed?


35. A certain sum is to be divide between A and B so that after 5 years the amount receivedby A is equal to the amount received by B after 7 years. The rate of interests is 10%,interest compounded annually. Find the ratio of amounts invested by them.

a) 121:144 b) 144:122 c) 2:3 d) 121:100 e) 100:121

www.OnlineIAS.com



ARITHMETIC36. A father divided Rs. 5100 between his two sons, Mohan and Sohan who are 23 and 24 at

present I such a way that if their shares are invested at compound interest @ 4% p.a.,will receive equal amount on attaining the age of 26 years. Find Mohan’s share.


37. A certain sum, invested at compound interest becomes Rs. 3000 in 3 years and Rs. 6000in 6 years. Find the amount after 9 years.

a) Rs. 7500 b) Rs. 9000 c) Rs. 10000 d) Rs. 12000 e) Rs. None

38. Population of a ten increases at a certain rate percent per annum. Present population ofthe town is 3600 and in 5 years’ time becomes 4800. How much will it be in 10 yearstime?

a) 5000 b) 6000 c) 6400 d) 7000 e) None

39. Present population of a town is 12000. Increasing at a certain rate, the population becomes27000 after six years. What will the size of population after 3 years from now?

a) 15000 b) 18000 c) 19500 d) 20000 e) None

40. find the difference between compound interest on Rs. 1000 for 1 ½ years at 20% p.a.when interest in compounded annually and half-yearly respectively.

a) Rs. 11 b) Rs. 10 c) Rs. 21 d) Rs. 20 e) NoneANSWERS FOR COMPOUND INTEREST

EXERCISE

1) b 2) e 3) e 4) e 5) c 6) a 7) c 8) e 9) b 10) e 11) a 12) e 13) c 14) b

15) c 16) a 17) a 18) b 19) a 20) c 21) b 22) a 23) a 24) b 25) a 26) b 27) a 28) b

29) e 30) c 31) c 32) b 33) c 34) e 35) d 36) b 37) d 38) c 39) b 40) a

www.OnlineIAS.com



ARITHMETIC

C.I AND S.I1. Difference between the S.I and C.I is ‘NIL’ for one year.2. If the difference between the S.I and the C.I for two years at R% p.a is d, then sum

2

410

R

dP

3. If the difference between the S.I and the C.I for three years at R% p.a is d, then sum

)300(

102

6

RR

dP

4. If the difference between the S.I and the C.I for four years at R% p.a is d, then sum

)60000400(

102

8

RRR

dP

5. If the difference between the S.I and the C.I for five years at R% p.a is d, then sum =

)1010500(

1075232

10

RRRR

dP

EXERCISE

1. Difference between Compound Interest and Simple Interest on Rs. 8000 for 2 years at10% p.a. is :

a) Nil b) Rs. 80 c) Rs. 160 d) Rs. 800 e) None

2. Find the difference between Compound Interest and Simple Interest on Rs. 4000 for 1year at 10% p.a. if the interest is compounded half – yearly.

a) Nil b) Rs. 5 c) Rs. 10 d) Rs. 40 e) Rs. 30

3. If difference between Compound Interest and Simple Interest on a certain amount at 5%p.a. for two years is Rs. 30. Find the Principal.

a) Rs. 10000 b) Rs. 12000 c) Rs. 12500 d) Rs. 15000 e) Nil

4. Two persons lent equal amount of money at 10% p.a. first at Compound Interest andsecond at Simple Interest. If first person gets Rs. 20 more than the second after a periodof 2 years. Find sum lent by each of them.


10. RELATION BETWEEN C.I AND S.I

www.OnlineIAS.com



ARITHMETIC5. Find the difference between Compound Interest and Simple Interest on Rs. 1000 for 3

years at 10% p.a., If interest ins compounded annually.


6. Find the difference between Compound Interest and Simple Interest on Rs. 10000 for 4years at 10% p.a. if interest is compound annually.


7. If Simple interest on a certain sum at 10% p.a. for 2 years is Rs. 80. The CompoundInterest on the same sum for the same period is:

a) Rs. 80 b) Rs. 82 c) Rs. 84 d) Rs. 88 e) Rs. 81

8. If Simple Interest on a certain sum for 2 years @ 10% p.a. is Rs. 200, the CompoundInterest will be?


9. If simple interest and compound interest on a certain sum for 2 years are Rs. 400 and Rs.440 respectively. What is the rate of interest?

a) 5% b) 10% c) 20% d) 25% e) data insufficient

10. If simple interest and compound interest on a certain sum for 2 years in Rs. 160 and Rs.168 respectively. What is the Principal?

a) Rs. 800 b) Rs 1600 c) Rs. 2000 d) Rs. 2500 e) data sufficient

11. On a certain sum, Compound Interest and simple interest for two years are Rs. 500 andRs. 520 respectively. Find the Principal.


12. The difference between Compound Interest and Simple Interest on a certain sum of moneyfor 3 years at 5% p.a. is Rs. 61. Find the Principal.


13. If simple interest for 3 years @ 10% is Rs. 300, then Compound Interest is:


14. If simple interest for 3 years @ 5% is Rs. 1200, Compound Interest is:


www.OnlineIAS.com



ARITHMETIC

ANSWERS FOR RELATION BETWEEN C.I. AND S.IEXERCISE

1) b 2) c 3) b 4) b 5) b 6) c 7) c 8) b 9) c 10) a 11) b 12) d 13) c 14) d

15) c 16) c 17) d 18) b 19) b

15. If Compound Interest on a certain sum for 2 years @ 5% p.a. is Rs. 328, the SimpleInterest will be?


16. If compound interest on a certain sum at 10% p.a. for 2 years is Rs. Rs. 210, find thesimple interest for same period on same amount.


17. If compound interest for a certain sum at 5% p.a. for 2 years is Rs, 492, find the simpleinterest for the same period on the same amount?


18. If compound interest on a certain for 3at 10is Rs. 662, find simple interest on that sum of3 years.

a) Rs. 570 b) Rs. 600 c) Rs, 625 d) Rs. 630 e) Rs, 670

19. If compound interest on a certain sum for 3 years at 20% is Rs. 728, find simple interestfor the same sum for 3 years.

a) Rs. 600 b) Rs. 650 c) Rs. 700 d) Rs. 700 e) Rs. 750

www.OnlineIAS.com



ARITHMETIC

If A can do a piece of work in x days, then he can do thx

1part of work in one day. Again If B

can do the same work in y days, he can do thy

1part of work in one day. If they two

together do the work they can do

yx

11 part of the work in one day. That is xy

yx th

part of the work in one day. Hence to do the full work they take yx

xy

th days. Similarly

if C also joins them, if he can do the work in z days. They three can complete the work

in days

zyx

1111

, i.e. zxyzxy

xyz

days. Their capacities will be in proportion with their

one day’s work. Hence the ratio of capacities of A and B is yx

1:

1 (or) y:x similarly the

ratio of capacities of A, B and C is zyx

1:

1:

1(or) yz:zx:xy..

The wages are paid according to their capacities. The more the capacity, the more than

wage. If the people working together get the total wage, amount is shared among the

people in the ratio of their capacities.

If the number of men to do a piece of work be changed in the ratio m:n then time taken by

them to finish the work in changed in the ratio n:m.

A is twice as good as a work man as B then

(i) Time taken by A and B are in the ratio 1:2

(ii) Work done by A and B are in the ratio 2:1

11. TIME AND WORK & PIPES AND CISTRENS

TIME AND WORK:

www.OnlineIAS.com



ARITHMETICPIPES AND CISTERNS:

If a tap fills in the tank with any liquid, the tap is called filling tap or inlet. If the tap emptiesthe tank, the tap is called empting tap or outlet. Some times inlets and outlets will worksimultaneously. Then the tank is filled in slowly. If the outlets empty more liquid thenfilling in liquid, it is not possible for the tank to be full for any long time. By the by if thetank contain liquid initially the tank will also be emptied gradually.

If two filling taps fill the tank in x hours and y then the tank will be full yx

xy

.

Hours: If at the same time, an empty pipe is also opened, then the part of the tank filled

in hour is zyx

1:

1:

1 whole z is the time in hours the emptying pipe empties the tank,

hence the tank will be full inzyx

1:

1:

11

hours.

EXERCISE

1. 20 men work can do a piece of work in 40 days, in how many days will 40 men do thesame work?

a) 20 days b) 40 days c) 60 days d) 80 days e) None

2. If 30 men can do a piece of work in 30 days, in how many days will 15 men do the samework?

a) 15 days b) 30 days c) 45 days d) 60 days e) 25 days

3. 12 men can do a piece of work in 15 days. How long will 10 men take to complete thework?


4. 12 men can do a piece of work in 15 days. How many men are required to complete thework in 10 days?

a) 10 men b) 12 men c) 15 men d) 18 men e) None

www.OnlineIAS.com



ARITHMETIC5. A work can be done by a certain number of workers in 8 days. How many days will they

take to finish a work four times the original work?


6. A and B together can type 35 pages in 5 minutes whereas A alone can type 20 pages in4 minutes. How many pages can B type in 1 minute?

a) 6 pages b) 5 pages c) 4 pages d) 2 pages e) None

7. A can do a piece of work in 15 days and B can do it in 10 days. Working together howlong will they take to finish the work?


8. A alone can do ½ of a work in 5 days and B alone can do 1/3 of the same work in 4 days.In how many days working together will they finish the work?

a) 16 4/5 days b) 32 days c) 24 days d) 15 days e) 5 5/11 days

9. A alone can do 1/5th of a piece of work in 3 days and B alone can 1/5th of the same workin 6 days. In how many days working together will they finish the work?


10. A and B can do a piece of work in 10 days while B alone can do it in 15 days. How longwill A along take to finish the work?

a) 20 days b) 30ays c) 24 days d) 12 days e) 6 days

11. A and B can do apiece of work in 12 days while A alone can do it in 20 days. How long willB alone take to finish the work?

a) 2 days b) 32 days c) 24 days d) 12 days e) 30days

12. A,B and C together can do a piece of work in 12 days. A and B together can do the samework in 20 days. In how many days C working alone can finish the work?


www.OnlineIAS.com



ARITHMETIC13. A alone can do a piece of work in 21days. B who is 40% more efficient than A, will finish

the work in:


14. A,B and C did a work together and earned Rs.729 for the work. If the ratio of work doneby A,B and C is 2:3:4, find C’s share


15. A alone can do a piece of work in 12 days and B alone in 10 days. They undertook to dothe work for Rs. 330. how much will A get?


16. A,B and C together undertook a work for Rs. 550 . A and B together done 7/11 of thework. Find C’s share.


17. A can do a piece of work in 10 days. With the help of B, he finished the work in 6 days.If they earn Rs. 200 for doing the job, find A’s share.


18. A, B and C can do a piece of work in 12, 18 and 30 days respectively. If they do a worktogether, find the ratio in which the amount is to be distributed.

a) 15:10:6 b) 15:10:7 c) 15:12:6 d) 17:10:6 e) None

19. A,B and C can do a piece of work in 12 days, B and C in 15 days respectively, In howmany days working together will they finish the work.


20. A and B and C can do a piece of work in 12, 15 and 20 days respectively. In how manydays working together will they finish the work.


21. A and B can do apiece of work in 20 days and 15 days respectively. With the help of C,they finished the work in 5 days. How many days will C alone take to finish the work?


www.OnlineIAS.com



ARITHMETIC22. A and B together can do 11/19 of a work, In the same time, B and C together can do 14/19

of the work. Find the ratio of work done by each of them.

a) 15:10:6 b) 2:10:7 c) 7:12:6 d) 1:10:6 e) 5:6:8

23. A and B can do a piece of work in 20 days. With the help of C, they finished the work in 15days. Find the time C alone will take to finish the work.


24. A alone can do a work in 4 days, B and C in 3 days, A and C in 2 days. How many days willB alone take to finish the work?


25. A and B can do a piece of work in 12 days, B and C can do the same work in 15 days. IfA is twice as good a worker as C, find the time that C alone will take to do the work.


26. A tap can fill a tank in 15 minutes while another tap can empty it in 20 minutes. If both thetaps are opened simultaneously, when the tank be full?

a) 30minutes b) 32 minutes c) 24 minutes d) 60 minutes e) 54 minutes

27. A pipe can fill a tank in 20 minutes. Due to leakage in the bottom of the tank, it takes 25minutes to ill the tank. If the tank is full, how long will the leak take to empty the tank?

a) 100 minutes b) 32 minutes c) 24 minutes d) 60 minutes e) 54 minutes

28. A cistern is normally filled in 9 hors but due to leak in the bottom, it takes one hours moreto be filled. If the cistern is full, in what time will the leak empty it?

a) 90 hours b) 14 hours c) 20 hours d) 60 hours e) 54 hours

29. A cistern is normally filled in 8 hours but it take s2 hors longer to fill because of a leak inthe bottom, If the cistern is full, in what time will the leak empty it?


www.OnlineIAS.com



ARITHMETIC30. A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are

opened. What is the total time taken to fill the tank completely?

a) 3 hrs 15 min b) 3 hrs 30 min c) 3 hrs 45 min d) 4 hrs 30 min e) None

31. A tap can empty a tank in 30 minutes while second tap empty it in 20 minutes. If both thetaps are kept open, how much time is required to empty the cistern?


32. Two pipes A and B can fill a tank in 12 hours and 16 hours respectively, while a third pipeC can empty the tank in 8 hours. If all the three pipes are opened simultaneously, thetank will be filled in:


33. Pipe A can fill a tank in 15 hours, B in 20 hours and C can empty the tank in 30 hours. Ifall the three taps are opened to together, how much time is required to fill the tank?


34. Pipe A can fill a tank in 15 min and pipe B can drain 40 liter per minute If both the pipesare opened together, the cistern is full in 45 minutes, find the capacity of the cistern.

a) 900 litres b) 850 litres c) 950 litres d) 1050 litres e) 1000 litres

35. A,B and C together can do a work in 4 days. If A and B do the work in 5 days, B and C in10 days, find the days taken by A and C to do the work.


36. A man and a woman working together can do a piece of work in 30 days. If they can dothe work in the ratio of 6:7, how many days will a man working alone ?


37. 2 men or 4 women can do a work in 28 days. How long will 4 men and 8 women take tocomplete the work?


www.OnlineIAS.com



ARITHMETIC38. 2 men or 4 women can do a work in 22 days. How long will 4 men and 3 women take to

complete the work?


38. 2 men or 4 women can do a piece of work in 30 days, in how many days can the work bedone by 2 men and 6 women?


39. If 2 men or 3 women can do piece of work in 30 days, in how many days can the work bedone by 2 men and 6 women?


40. 4 men and 7 women can do piece of work in 8 days. In how many days will 5 men and 2women finish the work if each women takes twice the time taken by one man?


41. 8 men can do piece of work in 5 days whereas 6 women can do the same work in 10days. In how many days can 4 men and 9 women finish the work?


42. If 2 men and 3 women can do a piece of work in 8 days and 3 men and 2 women in 7days. In how many days can the work be done by 5 men and 4 women working together?


43. A team consisting o 10 men and 9 women can do a piece of work in 9 days and anotherteam consisting of 8 men and 15 women in 8 days. In how many days can the work bedone by 16 men and 12 women?


44. A team consisting of 2 men and 5 women can do a piece of work in 12 days and anotherteam o f3 men and 7 women in 8 days can the work be done by 5 men and 12 womenworking together?

a) 4 days b) 4.8 days c) 6.4 days d) 10 days e) 12 days

www.OnlineIAS.com



ARITHMETIC45. 18 men and 12 boys can do a piece of work in 5 days. 9 men and 12 boys can do the

same work in 8 days. How many boys should assist 12 men so that the work is finishedin 6 days?

a) 4 boys b) 8 boys c) 16 boys d) 20 boys e) 18 boys

46. A man, a woman and a boy can do a work in 3, 4 and 12 days respectively. How manyboys must assist 1 man and 1 woman so as to finish the work in 1 day?

a) 3 boys b) 5 boys c) 10 boys d) 17 boys e) 18 boys

47. A, B and C working together can do a piece of work in 10 days. If A takes twice as longas B and C together, B takes thrice as long as A and C together, how many days will Calone take to finish the work?


48. A and B can do a piece of work in 15 days and 18 days respectively. A worked at it for 10days and then B finished the remaining work. Find the time taken by to finish the remainingwork?


49. A and B can do a piece of work in 15 days and 10 days respectively. Both work togetherfor 3 days and then A leaves off. In how many days will be work be completed?


50. A and B can do a work in 12 and 15 days respectively. They started the work together butA left after 4 days due to illness. The remaining work was finished by B in:


51. A and B together can do a work in 10 days. They worked together for 4 days and then bleaves off. A finished the remaining work in 18 days. In how many days, can A alone finishthe whole work?


www.OnlineIAS.com



ARITHMETIC52. Ram and Shyam can do a work in 8 days. Ram worked for 6 days and Shyam completed

the remaining work in 10 days. In how many days can Shyam alone finish the work?


53. Two pipes A and B can fill a cistern in 60 minutes and 48 minutes respectively. Both pipesare opened together. This cistern will be filled in half an hour, if the pipe B is turned offafter:

a) 6 minutes b) 18 minutes c) 20 minutes d) 24 minutes e) None

54. A and B together can do a work in 25 days, C alone can do it in 15 days. They workedtogether for 6 days and then c leaves off. In how many days will the remaining work befinished by A and B?


55. A and B can do a piece of work in 12 days and 20 days respectively. They started worktogether and then A left after working for some days. If the remaining work is finished byB in 12 days, how many days has A worked on it before leaving?


56. ‘A’ alone can do a piece of work in 6 days and b alone in 12 days. They started worktogether but 3 days before the completion of the work, A leaves. The work will be completedin:


57. A, B and C can do a piece of work in 10, 12 and 15 days respectively. They started thework together, but B leaves after 3 days. Find the days in which A and C will finish theremaining work?

a) 1 day b) 1.5 days c) 3 days d) 4.5 days e) 5 days

58. A, B and C together can finish a work in 12 days. They started the wrk together and thenA leaves after 4 days. If B and c took 10 days to finish the remaining work, in how manydays can ‘A’ alone do the work?


www.OnlineIAS.com



ARITHMETIC59. A, B and C can do a work in 12, 16 and 24 days respectively. They started the work

together but A left after working for 3 days and B left 3 days before the completion of thework. How many days would it take to finish the work?


60. ‘A’ alone can do a piece of work in 8 days and B alone can do the same work in 24 days.Working together they will finish the work in:


61. A and B can do a piece of work in 15 days and 30 days respectively. Working together,they will finish the work in:

a) 10 days b) 15 days c) 22.5 days d) 45 days e) None

62. A is 4 times good a workman as B. If A could finish a work in 15 days less than B, find thetime taken by them to finish the work while working together.

a) 4 days b) 5 days c) 6 days d) 7 ½ days e) None

63. A is twice as good a workman as B. Working together they can finish a work in 16 days.How many days will ‘A’ take to finish the work?


64. A is thrice as good a workman as B and together they finish a work in 24 days. In howmany days it can be done by B?


65. A does half as much work as B in one sixth of the time. If together they take 12 days tocomplete the work, how much time shall B take to do it alone?


66. A and B can do a work in 10 days and 15 days respectively. If they work at it on analternate day, A starting first, in how many days the work will be completed?


www.OnlineIAS.com



ARITHMETIC67. A, B and C can do a piece of work in 10, 30 and 60 days respectively. If A is assisted by B

and C on an alternate day, find number of days taken to finish the work.


68. Two men A and B can finish a work in 8 and 16 hours respectively. If they work on italternatively for one hour each, A beginning first, in how many hours will the work befinished?

a) 5 hours b) 5 ½ hours c) 10 hours d) 10 ½ hours e) None

69. Two pipes A and B can fill a cistern in 6 and 8 minutes respectively. If they be turned oalternatively for on minute each, how long will it take to fill the cistern?

a) 3 3/7 minutes b) 6 minutes c) 6 ¾ minutes d) 6 6/7minutes e) None

70. A and B can do a piece of work in 7 and 6 days respectively. If they work at it on analternate day. A starting first, in how many days the work will be complete?

a) 4 1/2 days b) 12 days c) 6 1/2 days d) 8 days e) None

71. Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, while third pipe Ccan empty the tank in 15 minutes. If the three taps are opened successively for oneminute each, how long will it take to fill the cistern?

a) 4 minutes b) 5 minutes c) 1 minutes d) 3 minutes e) 167

72. Two pipes A and B can fill a cistern in 15 and 20 minutes respectively, while third pipe Ccan empty the tank in 30 minutes. If the three taps are opened successively for oneminute each, how long will it take to fill the cistern?

a) 34 3/7 minutesb) 25 ¾ minutes c) 26 ¾ minutes d) 34 1/3 minutese) None

73. A certain number of men can complete a job in 60 days. If there are 8 more men, the workcan be completed in 10 days less. How many men were there originally?

a) 77 b) 80 c) 81 d) 83 e) 40

74. A certain number of men can complete a job in 0 days. If 10 men are absent, the remainingman can do the work in 12 days. How many men were there originally?

a) 30 b) 40 c) 10 d) 20 e) 60

www.OnlineIAS.com



ARITHMETIC75. If 18 men working 7 hours a day can finish a work in 24 days. In how many days 21 men

working 8 hours pr dya ill finish the same work?


76. If 60 men working 7 hours a day can do apiece of work in 18 days, in how many days will21 men working 8 hours a day can do the same work?


77. If 100 men can do 100 work in 100 days. How long will it take 1 man to do 1 work?

a) 4 1/2 days b) 12 days c) 6 1/2 days d) 8 days e) 100 days

78. If 15 workers can earn Rs. 1800 in 10 days. Find the earning of 5 workers in 8 days.


79. If 40 men working 9 hours a day can do apiece of work in 24 days. How many menworking 8 hours a day can do double that work in 60 day?

a) 44 b) 56 c) 64 d) 70 e) 36

80. If 30 labors working 5 hours a day can make a 300 meters long road in 32 days, how longwill it take 20 labors to make the 100 meters long road working 8 hours a day?

a) 4 1/2 days b) 12 days c) 6 1/2 days d) 8 days e) 10 days

81. A contractor agreed to complete a work in 120 days. He engaged 150 men for the workand after 70 days, only half of the work was completed. How many additional men musthe employ to complete the work in agreed time?

a) 80 b) 60 c) 64 d) 70 e) 36

82. A contractor agreed to complete a work in 40 days. He engaged 25 men for the work andafter 24 days, only one-third of the work was completed. How many more men must heemploy to complete the work 4 days earlier?

a) 72 b) 75 c) 94 d) 70 e) 36

83. A garrison of 850 men has provision for 26 weeks. If at the end of 6 weeks, they arereinforced by 150 men, how long will the provision last now?

a) 7weeks b) 8 weeks c) 9 weeks d) 4 weeks e) 17 weeks

www.OnlineIAS.com



ARITHMETIC84. A camp has provision of food for 600 persons for 41 days. After 37 days, 360 persons left

the camp. How long the food will last for the remaining persons?

a) 4 days b) 12 days c) 6 1/2 days d) 8 days e) 10 days

85. A fort has provision for 50 days. If after 10 days, they are re-enforced by 500 men and theremaining food lasts 35 days, how many ken wee there in the fort initially?

a) 300 b) 4000 c) 1000 d) 3500 e) 3060

86. 12 men can do ½ of a work in 15 days. In how many days will 10 men finish the work?


87. ‘A’ alone can do a piece of work in 90 days. He works at it for 15 days and then B alonefinishes the remaining working together they will finish the work in:


88. A, B and C together can do a work in 8 days. If B takes double time of A, C takes doubletime of B, find the time taken by ‘A’ alone to do the work.


89. A can do a piece of work in 80 day. He alone works at it for 20 days and then B alonefinished the remaining work in 36 days. In how many days A and B together can completethe work?


90. A and B can do a piece of work in 30days. They worked together for 6 days and A leavesoff. If B finishes the remaining work in 36 days, how many days will A alone take to do thework?


91. 25 men can do a piece of work in 17 days. They worked at it for 5 days and then somemore men joined the group and all of them together finished the remaining work in 10days. How many more men joined the group?

a) 5 men b) 6 men c) 7 men d) 8 men e) None

www.OnlineIAS.com



ARITHMETIC92. A can do a certain work in the same time in which B and C together can do it. If A and B

together could dot it in 10 days and C alone in 50 days, then B alone could to the workin:


93. 25 men can finish a work in 150 days. They started the work and at the end of every 10days, 25 additional men are employed. In how many days will the work be finished?


94. A and B working together can do a piece of work in 12 days, B and C together can do thework in 16 days. A alone started the work and worked on it for 5 days. Then B aloneworked on it for 7 days. Now C finishes the remaining work in 13 days. How many dayswill B alone take to do the work?


ANSWERS FOR TIME AND WORK & PIPES AND CISTERNS

EXERCISE

1) a 2) d 3) c 4) d 5) b 6) d 7) e 8) e 9) a 10) b 11) e 12) b 13) b 14) d

15) a 16) a 17) a 18) a 19) a 20) c 21) d 22) e 23) e 24) d 25) e 26) d 27) a 28) a

29) c 30) c 31) c 32) b 33) b 34) a 35) a 36) d 37) a 38) b 39) c 40) d 41) c 42) a

43) c 44) b 45) c 46) b 47) b 48) b 49) b 50) e 51) d 52) c 53) d 54) a 55) a 56) d

57) b 58) a 59) d 60) b 61) a 62) a 63) c 64) d 65) e 66) c 67) c 68) d 69) c 70) c

71) e 72) d 73) e 74) e 75) b 76) a 77) e 78) d 79) e 80) e 81) b 82) b 83) e 84) e

85) d 86) c 87) a 88) a 89) b 90) d 91) a 92) c 93) b 94) d

www.OnlineIAS.com



ARITHMETIC

Distance = speed time

Distance is in direct proportion with speed and time while speed and time are in indirectproportion.

Speed =time

Distence; Time = speed

Distence

If the distance, velocity (speed) and time taken are represented by d1v1t1 respectively, then

1. For distance constant v1t1=v2t2 (or) v1: t1=v2: t2

2. For time constant :2

1

2

1

v

v

d

d

3. For speed constant :2

1

2

1

t

t

d

d

Note: If the speed is given in km/hr multiply the number by 5/18 to get speed is m/sec.Similarly If m/sec means 18/5 km/hr.Relative speed: If two things are in motion and moving in a straight live either in oppositedirection or some direction, to find their time of meeting we have to find their relativespeed. In the first case, the relative speed is equal to the sum of their speeds and in thesecondcase, the relative sped is equal to the difference of their speeds. Initially if two persons are atA and B and more in a straight line, then the time taken for them to meet = distance betweenthem their relative speedEXERCISE

1. A train is running at the average speed of 90 km/h, its speed in meters per second is:

a) 25 m/s b) 50 m/s c) 90 m/s d) 324 m/s e) None

2. A train is running at the average speed of 10 m/s, its speed in km/h is:

a) 27.7 km/h b) 36 km/h c) 60 km/h d) 72 km/h e) None

3. A train running at the average speed of 30 km/h covers a distance in 6 hours. Find thespeed of another train which covers the same distance in 5 hours.

a) 24 km/h b) 25 km/h c) 36 km/h d) 42 km/h e) None

12. TIME AND DISTANCE

www.OnlineIAS.com



ARITHMETIC4. Train A took 35 minutes to cover a distance of 50 km. If the speed of train B is 25% faster

than train A, it will cover the same distance in:


5. Two persons start walking in opposite directions at 5 km/h and 4 km/h respectively. Afterhow many hours will they be 45 km apart?

a) 5 hours b) 7 hours c) 9 hours d) 11 hours e) None

6. Two persons start walking in the same direction at 5 km/h and 4 km/h respectively. Inhow many hours will they be apart?

a) 5 hours b) 7 hours c) 9 hours d) 11 hours e) 45hours

7. A man takes 8 hours in walking to a certain place and riding back. He would have gained2 hours by riding both ways. What time would he take to walk both ways?


8. A 100 meter long train takes 5 seconds to pass a standing man. Find the time taken bythe train in crossing a railway platform of 260 meter in length.

a) 18 seconds b) 13 seconds c) 26 seconds d) 36 seconds e) None

9. A train running at the average speed of 45 km/h passes a standing man in 10 seconds.Find the length of the train.

a) 75 meter b) 100 meter c) 125 meter d) 150 meter e) None

10. Find the time taken by a 200 meter long train, running @ 72 km/h in crossing a standingman.

a) 8 seconds b) 10 seconds c) 12.5 seconds d) 20 seconds e) None

11. A 250 meter train is running at the average speed of 90 km/h. how ling will it take to passa standing man.


www.OnlineIAS.com



ARITHMETIC

12. Find the time taken by a 100 meter long train to cross a platform of 400 meter in length,if the train is running @ 90 km/h.

a) 12.5 seconds b) 15 seconds c) 20 seconds d) 25 seconds e) None of these

13. A train running a the speed of 15 m/s takes 20 seconds to pass a man running at thespeed of 5 m/s in the same direction. Find the length of the train.


14. A train running at the speen of 25 m/s takes 10 seconds to pass a man running at thespeed of 10 m/s in the opposite direction. Find the length of the train.


15. A 150 meter long train running at the speed of 36km/h crosses a man walking in thesame direction at an average speed of 7 km/h in:

a) 12 seconds b) 13 seconds c) 15 seconds d) 14 seconds e) None of these

16. A 150 meter long train running at the speed of 36 km/h takes 30 seconds to cross aplatform completely. Find the length of the platform.


17. A 150 meter long train crosses a 150 meter long platform, in 15 seconds. What is thespeed of the train?


18. A train running at uniform sped passes a standing man in 2 seconds and a platform of 50meter in length n 3 seconds. Find the length of the train.


19. A train crosses a pole in 10 seconds and a 150 meter long platform in 16 seconds. Thespeed of the train in km/h is:


www.OnlineIAS.com



ARITHMETIC

20. Two trains of the length of 139 meter and 111 meter are running in the opposite directionsat the speed of 53 km/h and 37 km/h respectively. In what time will they completelycross each other?

a) 5 seconds b) 7.5 seconds c) 10 seconds d) 15 seconds e) None

21. Two trains of length of 123 meter and 147 meter running in the same direction at thespeed of 59 km/h and 23 km/h respectively. In what time will they completely cross eachother?


22. A man ha to cover a distance of 30 km in 8 hours. He could cover only 2/3 rd of thedistance in ¾ th of the time. At what speed should he cover the remaining journey so asto reach his destination on time?


23. A 200 meter long train is running at an average speed of 75 km/h and the other 250 meterlong train is running in the opposite direction at an average speed of 33 km/h. Find thetime they will take to cross each other.

a) 15 km/hr b) 20 km/hr c) 30 km/hr d) 35 km/hr e) None of these

24. Two trains are running in the same direction at 74 km/h and 38 km/h. If the faster traincrosses a man sitting in the slower train in 15 seconds, find the length of the faster train.

a) 15 m b) 20 m c) 30 m d) 35 m e) None of these

25. A 100 meter long train passes a man going in the opposite direction at the speed of 5 km/h in 9 seconds. Find the speed of the train in km/h

a) 60 km/h b) 90 km/h c) 120 km/h d) 180 km/h e) 35 km/h

26. A and B walk around a circular path of 900 meter in circumference, starting together fromthe same point in the same direction. If their speeds are 150 meter per minute and 200meter per minute respectively, after how many minutes will they be again at the staringpoint?


www.OnlineIAS.com



ARITHMETIC27. A and B walk around a circular path of 5km in circumference, starting together from the

same point in the same direction. If their speeds are 4 km/h and 3km/h respectively, afterhow many hours will they be again at the starting point?


28. A and B can walk around a circular path in 4 hours and 6 hours respectively. If they startfrom the same point in the same direction, when will they be together at the starting pointagain?


29. A man is walking at a speed of 10 km/h. After every km, he takes rest for minutes. Howmuch time will he take to cover a distance of 10 km?


30. Two men A and B walk from P to Q, a distance of 21 km at 3 km/h and 4 km/h respectively,B reaches at point Q and returns immediately and he meets A at point R. Find thedistance from P to R.

a) 24 km b) 25 km c) 36 km d) 42 km e) 18 km

31. Two men A and B walk from P to Q, a distance of 36 km at 7 km/h and 5km/h respectively.A reaches at Q and immediately returns and meets B at a place R. Find the distancebetween P and R.


32. Train A takes 6 hours more than train B to cover a distance of 800 km. If the speed of trainA is doubled it takes 2 hours less than train B. What is the speed of train B?


33. A man standing on a railway platform notices that a train going in one direction takes 10seconds to pass him and other train of the same length takes 15 seconds to pass him.Find the time taken by the two trains to cross each other when they are running in theopposite directions.

a) 15 seconds b) 20 seconds c) 30 seconds d) 35 seconds e) 12 Seconds

www.OnlineIAS.com



ARITHMETIC34. A man standing on a railway platform notices that a train going in one direction takes 9

seconds to pass him and other train of the same length takes 6 seconds to pass him.Find the time taken by the two trains to cross each other when they are running in thesame direction?

a) 30 seconds b) 36 seconds c) 38 seconds d) 35 seconds e) 12 Seconds

35. Two trains running in the opposite directions at the speeds o 44 km/h and 55 km/h take12 seconds to cross each other. If the length of one train is 150 meter, what is the lengthof the other train?


36. Two trains of 175 meter and 2250 meter cross a pole in 7seconds and 10 secondsrespectively. In what time will they cross each other, if they are running in the oppositedirection?


37. Two trains running in the same direction at the speeds of 68 km/h take 36 seconds tocross each other. If the length of one train is 85 meter, what is the length of the othertrain?


38. A 220 meter long train running at 90 km/h crosses a 180 meter train coming from theopposite direction in 9 seconds. The speed of the second train is:


39. Two trains of length os 250 meter and 200 meter are running in the same direction. If thetrains cross each other in 45 seconds and the speed of the first train is 27 km/h, findspeed of the second train.


40. two trains of the length of 200 meter and 250 meter are running in the opposite directionsat the speed of 35 km/h and 55 km/h respectively. Find the time in which the faster trainwill pass a man sitting in the slower train.

a) 2 seconds b) 8 seconds c) 10 seconds d) 18 seconds e) 20 seconds

www.OnlineIAS.com



ARITHMETIC

41. Two train start at the same time from station A and B towards station B and A at thespeed of 50 km/h and 55 km/h respectively. When the two trains meet it is found that thefaster train has traveled 30 km more than the slower one. What is the distance betweenthe two stations.


42. Two trains start at the same time from station and proceed towards each other at thespeed of 15 km and 20 km per hour respectively. When the trains meet, it is found thatone train has traveled 50 km more than the other. Find the distance between the twostations.


43. Two trains start at the same tome from station A and B towards each other. Distancebetween the two stations is 420 km and the trains meet each other after 6 hours. If thedifference between speeds of two trains is 10 km/h, find the speed of the slower train.


44. Two trains start at the same time from two stations 360 km apart. If the trains meet after5 hours and difference between their speeds is 12 km/h, find the speed of the faster train.


45. A 150 meter long train passes a sanding man in 15 second. While it crosses anothertrain of the same length coming from the opposite direction in 12 seconds. Find thespeed of the second train.


46. Two trains start the same time from two stations 117 km apart and proceed towards eachother. If the ratio of speeds of the two trains is 4:5 and the speed of the first train is 60 km/h, find the time after which the two trains will meet.


47. A train is running at 70 km/h but due to stoppages it could cover a certain distance at 63km/h. How much time the train stops on an average (per hour)?


www.OnlineIAS.com



ARITHMETIC

48. Two trains measuring 120 meter and 180 meter cross each other completely in 10 secondswhen running in opposite directions and the faster train takes 30 seconds to cross theslower train when the two trains are running in the same direction. Find the speed of thefaster train.


49. The distance between two stations A and B is 300 km. One train leaves station A towardsstation B at the average speed of 100 km/h. At the same time, another train leavesstation B towards A at the average speed of 80 km/h. The distance from station A wherethe two trains meet is:


50. The distance between two stations A and B is 550 km. One train leaves station A towardsstation B at the average speed of 100 km/h. After half an hour, another train leaves stationB towards A at the average speed of 150 km/h. The distance from station A where the twotrains meet is:

a) 100 km b) 200 km c) 250 km d) 300 km e) None

51. A and B start from X and Y towards Y and X respectively. If they cover the distance in 4and 6 hours respectively, when will they meet?

a) 2 hours 24 minutes b) 2 hours 40 minutes

c) 5 hours d) 10 hours e) None

52. A starts from X towards Y at 10 a.m. B starts from Y towards X at 11 a.m. If they reachtheir destinations at 2 p.m. and 5 p.m. respectively, at what time will they meet?

a) 12.24 p.m. b) 12.48 p.m. c) 1.48 p.m. d) 2.24 p.m. e) None

53. A man starts walking from A to B. at the same time another man starts from B to A. Afterpassing each other, they complete their journey in 9 and 4 hours respectively. At whatspeed is the second man walking, if the first walks at 6 km/h.


www.OnlineIAS.com



ARITHMETIC

54. A theft is reported to a policeman. The thief starts running and the policeman chaseshim. When the policeman starts chasing, the thief was at a distance of 250 meter. Thethief and the policeman run at the speed of 8 km/h and 9 km/h respectively. Find the timethe policeman will take to catch the thief.


55. A train leaves station A towards B at an average speed of 60 km/h at 9 a.m. After 2 hoursanother train leaves station A at an average speed of 100 km/h. When the two trains willmeet?

a) 11 a.m. b) 1 p.m. c) 2 p.m. d) 3 p.m. e) None

56. Two guns were fired from the same place at an interval of 12 minutes. A person approachingthe firing place in his car hears second shot 11 minutes after the first. If the speed ofsound is 220 m/s, find the speed of the car.


57. A train leaves station A towards B at an average speed of 80 km/h. After 3 hours anothertrain leaves station A at average speed of 110 km/h Find the distant from station A wherethe 2 trains meet.


58. A man walking at ¾ of the speed, reaches his office late by 2 hours. What is the usualtime.


59. Walking at 5/4 of the usual speed, I reach my office 12 minutes to early. What is theusual time?


60. If a man goes to a place at an average speed of 10 km/h and then returns at the averagespeed of 15 km/h. Find his average speed during the whole journey.


www.OnlineIAS.com



ARITHMETIC

61. If a man covers half his journey at an average speed of 60 km/h and the reaming at 40km/h, What is his average speed during the whole journey.


62. A man goes to his office at the speed of 8 km/h and returns at the speed of 12 km/h. If hetakes 10 hours in all. Find total distance covered by him.


63. A man goes to his office at the speed of 5 km/h and returns at the speed of 20 km/h. If hetakes 4 hours in all. The distance between the residence and office is


64. A man covers 1/3rd office journey at 60 km/h, next one by 1/3rd office journey at 30 km/h, and reaming 1/3rd journey at 10 km/h. Find his average speed during the journey.


65. A man travels 28 km at 7 km/h, next 16 km at 4 km/h and reaming 6 km at 3 km/h. Findhis average speed during the journey?


66. If I walk @ 4 km/h, I reach the office 5 minutes late and if I walk @ 5 km/h, I reach 10minutes early. How far my office is


67. If I walk @ 20 km/h, I reach the office 11 minutes late and if I walk @ 25km/h, I reach 19minutes early. What is the distance between residence and office


68. A train running at an average speed of 45 km/h reaches its distance in time. If the traingoes at average speed of 40 km/h, It reaches late by ½ hours. The total distance is :


www.OnlineIAS.com



ARITHMETIC

69. A man goes to a certain place @ 50 km /h by his car. Had he covered the journey @ 60km/h, He would have cover the distance in two hours less. Find the distance between thetwo places.

a) 500 km b) 600 km c) 700 km d) 160 km e) 900km

70. A and B start together to run a certain distance, A at 30 km/h and B at 20 km/h. Find thedistance, If A arrives 15 minuets before B.


71. A train moving at the speed of 40 km/h tales 2 hours more to cover a certain distancethan a train moving at 60 km/h. Find the distance:


72. Two cyclists A and B cover a certain distance. A reaches to destination 1 hours before B.Even if B had given a star of 5 km, He would have reached 10 minutes. Find the speed ofB.

a) 5 km/hr b) 6 km/hr c) 7 km/hr d) 16 km/hr e) 9 km/hr

73. Two cyclists A and B cover a certain distance of 110 km. A reaches to destination 1 hoursbefore B. Even if B had given a star of 8 km, He would have reached 12 minutes late. Findthe speed of A.


ANSWERS FOR TIME AND DISTANCEEXERCISE

1) a 2) b 3) c 4) b 5) a 6) e 7) d 8) a 9) c 10) b 11) b 12) c 13) c 14) d

15) a 16) c 17) c 18) d 19) b 20) c 21) d 22) e 23) a 24) e 25) e 26) e 27) a 28) a

29) e 30) e 31) d 32) d 33) e 34) b 35) b 36) c 37) a 38) b 39) c 40) c 41) e 42) c

43) a 44) c 45) d 46) b 47) a 48) d 49) b 50) b 51) a 52) b 53) c 54) b 55) c 56) d

57) a 58) e 59) d 60) d 61) b 62) e 63) c 64) e 65) c 66) a 67) b 68) c 69) b 70) a

71) c 72) b 73) d

www.OnlineIAS.com



ARITHMETIC

Boat is said to be moving downstream when it is going with the streamand it is said to be going upstream when it is going against the stream. If speed of a boatin still water is ‘x’ km/h and speed of the stream is ‘y’ km/h, speed of the boat downstream = (x+y) km/h And Speed of the boat upstream = (x-y)km/h.If we are given speed of boat upstream and downstream then we can find speed of boat instill water and speed of stream as follows:

Speed of boat in still water 1= Downstream+Upstream2

Speed of stream 1= Downstream-Upstream2

EXERCISE

1. A man can row a boat 12 km/h with the stream and 8 km/h against the stream. Find hisspeed in still water:


2. A man can row a boat 27 km/h with the stream and 11 km/h against the steam. Findspeed of stream.


3. A man can row a boat 15 km/h with the current and speed of current is 3 km/h. Find hisspeed against the current.


4. The speed of a boat in still water is 12 km/h and its speed against the current is 8.5 km/h. Find the speed of boat with the current.

a) 16.7 km/h b) 14.4 km/h c) 15.5 km/h d) 17.7 km/h e) 19.3 km/h

5. A man can row a boat 40 km downstream in 5 hours and 18 km upstream in 3 hours. Findthe speed of the current


6. A man can row downstream 35 km and upstream 15km taking 5 hours each time. Whatis speed of the current?


13. BOATS AND STREAMS

www.OnlineIAS.com



ARITHMETIC7. A man can row a boat 120 km with stream in 5 hours. If speed of the boat is double the

speed o the stream, find the sped of stream.


8. On a river, B is equidistant from both ends A and C. If a boat can go from A to B and backin 6 hours and from A to C in 8 hours, how long would it take to go from C to A?


9. A man rows a boat from point A against current for 10 minutes and then comes back withthe current for next 10minutes and reaches to a point B. If distance between A and B is1 km, find the speed of the current.


10. A man rows a boat 3 hours downstream, and 3 hours upstream. Find speed of boat in stillwater, if he covers a total distance of 12 km.


11. Speed of a boat in still water is 16 km/h. If it can travel 20 km downstream in the sametime as it can travel 12 km upstream, the rate of stream is.


12. A man can row a boat at 12 km/h in still water. If he takes twice the time to go upstreamas to row downstream, find the sped of the boat upstream.


13. A man can row a boat to a certain distance upstream in 4 hours and takes 3 hours to rowdownstream the same distance. What is the speed o boat in still water, if the speed ofthe stream is 2 km/h.


14. A man can row a boat to a certain distance upstream is 20 hours and the same distancedownstream in 12 hours. What is the speed o boat in still water, if the speed of thestream is 6 km/h?


15. A man can row a boat at 6 km/h in still water and speed of the current is 2 km/h. If hetakes 45 minutes to row the boat to a place and back. Find the distance between the twoplaces.


www.OnlineIAS.com



ARITHMETIC16. A man can row a boat at 5 km/h in still water and speed of the current is 1 km/h. He takes

5 hours to row boat to a place and come back to the starting point. Find the distancebetween the two places.


17. A man rows boat to a place covering 72 km distance and back in 15 hours. He finds thathe can row 3 km with the stream in the same time as 2 km against the stream. Find thespeed of the stream.


18. The speed of a boat in still water is 12 km/h and the speed of the stream 3 km/h. If totaltime taken to travel from A and B and back is 8 hours. Find the distance between And B


19. A boat whose speed in the still water is 16 km/h, covers a distance of 30 km upstreamand then returns taking 4 hours in total. What is the speed of the current?


20. The speed of current is 5 km/h. A boat goes 10 km upstream and then returns to thestarting point is 50 minutes. What is the speed of boat in still water?


ANSWERS FOR BOATS AND STREAMSEXERCISE

1) a 2) e 3) e 4) c 5) e 6) c 7) e 8) b 9) d 10) c 11) b 12) c 13) b 14) d

15) d 16) d 17) c 18) b 19) b 20) d

www.OnlineIAS.com



ARITHMETIC

EXERCISE1. Five years ago, A was 10 years younger than B. What will be the difference between their

ages after 2 years from now?a) 3 years b) 8 years c) 10 years d) 15 years e) None

2. Ratio of present ages of A and B is 2:3. After 6 years, ratio of their ages is 3:4. Find thepresent age of A.a) 6 years b) 12 years c) 18 years d) 24 years e) None

3. In 30 years, age of a person becomes 3 times of his present age. What is his presentage?a) 7.5 years b) 10 years c) 12.5 years d) 15 years e) None

4. Mohan got married 9 years ago. Today his age is 1 1/3 times of his age at the time of hismarriage. Find his present age.a) 12 years b) 27 years c) 36 years d) 45 years e) None

5. The sum of ages of Mohan and his father is 35 years. When Mohan’s age will be equal topresent age of his father, then sum of their ages will be 85 years. Find present age of thefather.a) 20 years b) 25 years c) 30 years d) 32 years e) None

6. The sum of ages of Sunil and his father is 46 years. 3 years back father’s age was 4times Sunil’s age. Find present age of Sunil.a) 7 years b) 8 years c) 11 years d) 12 years e) None

7. The sum of ages of Suresh and his father is 78 years. 6 years hence fathers age will betwice of Suresh’s age. Find present age of father.a) 30 years b) 52 years c) 54 years d) 60 year e) None

8. A’s age is 50 years and B’s age is 18 years.In how many years will be twice as old as B?a) 14 years b) 15 years c) 16 years d) 18 years e) None

9. Sum of present age of A, B and C are 72 years. If 4 years ago, their ages were in the ratioof 1:2:3, find A’s present age.a) 7 years b) 10 years c) 12 years d) 14 years e) None

10. Sum of present ages of A and B is 60 years. 5 years hence their ages will be in the ratioof 3:4, Find A’s present age.a) 25 years b) 30 years c) 35 years d) 40 years e) None

11. The ages of A and B are in the ratio 8:5. If sum of their ages is 39 years, what will be theratio of their ages after 9 years?a) 3:2 b) 8:7 c) 10:7 d) 11:8 e) None

12. At the time of marriage, a man was 6 years elder to his wife. 12 years after their marriage,his age is 6/5 times the age of his wife. What was wife’s age at the time of marriage?a) 18 years b) 24 years c) 30 years d) 36 years e) None

13. Present age of Ram’s father is 4 times Ram’s age. 5 years from now, father’s age willbecome 3 times of Ram’s age, find present age of Ram’s father.a) 40 years b) 45 years c) 50 years d) 60 years e) None

14. PROBLES ON AGES

www.OnlineIAS.com



ARITHMETIC14. A and B are 3 years and 2 years old respectively. Their father is 40 years old. After how

many years, father’s age would be twice of combined age of A and B?a) 5 years b) 10 years c) 15 years d) 20 years e) None

15. If ratio of Mohan’s age to that of his father is 1:5. After 10 years, their ages will be in theratio of 1:3. What is the father’s present age?a) 25 years b) 30 years c) 40 years d) 50 years e) None

16. Ratio of present ages of father and son is 8:3. If 10 years from now, the ratio becomes 2:1find present age of the son.a) 15 years b) 20 years c) 40 years d) 55 years e) None

17. 3 years ago, the age of father was 7 times of his son’s age. If the father’s present age is 5times his son’s age. Find the present age of the father.a) 35 years b) 39 years c) 42 years d) 45 years e) None

18. Ratio between present ages of A and B is 3:4. What is the present age of A, if 4 years ago,the ratio was 5:7?a) 20 years b) 24 years c) 28 years d) 32 years e) None

19. 5 years ago, the father’s age was 3 times of his son’s age. 5 years hence the 5 ratiobetween the ages of father’s and the son becomes 11:5. Find the father’s present age.a) 40 years b) 45 years c) 50 years d) 55 years e) None

20. 2 years ago, the father’s age was 6 times of his son’s age. Years hence the ratio betweenthe ages of father and the son becomes 10:3. What is the father’s present age?a) 40 years b) 42 years c) 44 years d) 48 years e) None

21. 3 years ago, a father’s age was twice the ages of his 4 sons. In 3 years time, the father’sage will be equal to sum of ages of the sons. Find the present age of fathera) 24 years b) 36 years c) 39 years d) 45 years e) None

ANSWERS FOR PROBLEMS ON AGESEXERCISE

1) c 2) b 3) d 4) c 5) c 6) c 7) c 8) a 9) d 10) a 11) d 12) a 13) a 14) b

15) d 16) a 17) d 18) b 19) c 20) c 21) c

www.OnlineIAS.com



ARITHMETIC

The clock has t wo hands – smaller hand and bigger hand. The smaller hand is calledHour Hand and the bigger hand is called Minute Hand . In one hour, the minute hand covers 60minutes spaces whereas the hour hand covers 5 minute space. It means that in 60 minutes,the minute hand gains 55 minute over the hour hand. The 55 minute space over the hour hand,the minute hand takes 60 minutes To gain 1 minute space over the hour hand, the minutehand takes 60/55 or 12/11 minutes.We multiply 12/11 with total minutes to be gained overthe hand hour.

We can do this by multiplying the number by11+

11

The Minute Hand moves 60 per minute and the hour hand move12

0

per minute.

Hence Minute Hand gains152

0

per minute.

CLOCK1. Speed of the hours hand = 0.50 per minute.2. Speed of the minutes hand = 60 per minute3. Speed of the seconds hand = 3600 per minute

4. MH2

1130 S.NO

when H = HoursM = Minutes = angle between hours and minutes hands.

5. 1 minute = 60

6. A clock strickes for 156 times in a day excluding half an hour strickings.7. A clock strickes for 180 times in a day including half an hour strickings.8.

9. Hands indicating opposite directions means having 1800 between then.10. Hands lying on the same straight line means having 0 or 180 between then.11. The sum of the times in a clock and in its mirror image is 12 hours.12. For every 65 5/11 minutes the hands of the clock coinside milt each other.

S.NO

123

Angle beteween the hours handand the minutes hand in degrees

0900 36090

Number of time in a day

224422

15. CLOCKS

www.OnlineIAS.com



ARITHMETIC

EXERCISE1. At what time between 5 and 6 are the hands of clock coincident ?

1) 22 minutes past 5 2) 30 minutes past 53) 88 2/11 minutes past 5 4) 27 3/11 minutes past 5 5) None

2. At what time between 9 and 10 will teh hands of a watch be together ?1) 45 minutes past 9 2) 40 minutes past 93) 49 1/11 minutes past 9 4) 48 2/11 minutes past 9 5) None

3. At what time between 7 and 8 will the hands of a clock be in the same straight line, but nottogether ?1) 5 minutes past 7 2) 5 2/11 minutes past 73) 5 3/11 minutes past 7 4) 5 5/11 minutes past 7 5) None

4. At what time between 4 and 5 will the hands of a watch point in opposite directions ?1) 45 minutes past 4 2) 40 minutes past 43) 50 4/11 minutes past 4 4) 54 6/11 minutes past 4 5) None

5. At what time between 5.30 and 6 will the hands of a clock be at right angles ?1) 43 5/11 minutes past 5 2) 43 7/11 minutes past 53) 40 minutes past 5 4) 45 minutes past 5 5) None

6. At watch, which gains uniformly, is 2 min. slow at noon on Monday, and is 4 min. 48seconds fast 2 p.m on the following Monday. When was it correct ?1) 2 p.m. on Tues day 2) 2 p.m. on Wednesday3) 3 p.m. on Thursday 4) 1 p.m. on Friday 5) None

7. At watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of thesame day, when the watch indicated quarter past 4 O’clock, the true time is :1) 59 7/12 minutes past 3 2) 4 p.m3) 58 7/11 minutes past 3 4) 2 3/11 minutes past 4 5) None

8. How much does a watch gain or lose per day, if its hands coincide every 64 minutes1) loses 96 minutes 2) loses 90 minutres3) loses 36 5/11 minutes 4) loses 32 8/11 minutes 5) None

9. How many times do the hands of a clock coincide in a day ?1) 24 2) 20 3) 21 4) 22 5) None

10. How many times do the hands of a clock point towards each other in a day ?1) 24 2) 20 3) 12 4) 22 5) None

11. How many times are the hands of a clock at right angles in a day ?1) 24 2) 48 3) 22 4) 44 5) None

12. How many times in a day, are the hands of aclock straight ?1) 24 2) 48 3) 22 4) 44 5) None

13. At what angble the hands of a clock are inclined at 15 minutes past 5 ?1) 72 1/2 2) 67 1/2 3) 58 1/2 4) 64 5) None

www.OnlineIAS.com



ARITHMETIC

14. At what time between 3 and 4 O’clock are the hands of a clock together ?1) 16 4/11 minutes past 3 2) 16 4/11 minutes past 43) 16 5/11 minutes past 3 4) 15 4/11 minutes past 3 5) None

15. At what time between 4 and 5 O’clock will the hand of clock be at right angle ?1) 38 1/11 minutes past 4 2) 38 2/11 minutes past 43) 38 1/11 minutes past 5 4) 38 5/11 minutes past 4 5) None

16. Find at what time between 8 and 9 O’clock will the hands of a clock be in the samestraight line but not together.1) 50 1/11 minutes past 8 2) 50 1/11 minutes past 93) 50 10/11 minutes past 8 4) 50 1/11 minutes past 10 5) None

17. At what time between 5 and 6 are the hands of a clock 3 minutes apart ?1) 24 minutes past 5 2) 25 minutes past 33) 23 minutes past 4 4) 30 minutes past 6 5) None

18. The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of correcttime. How much a day does the clock gain or lose ?1) 10 10/ 153 min 2) 10 12/143 min3) 10 10/143 min 4) 14 10/143 min 5) None

19. Awatch which gains uniformly, is 5 min. slow at 8 O’clock in the morning on Sunday, andis 5 minutes 48 seconds fast at 8 p.m. on following Sunday. When was it correct ?1) 20 min. past 7 p.m. on Wednesday2) 22 min. past 7 p.m. on Wednesday3) 20 min. past 7 p.m. on Thursday4) 20 min. past 8 p.m. on Wednesday5) None.

ANSWERS OF CLOCKS

1) d 2) c 3) d 4) d 5) b 6) b 7) b 8) d 9) d 10) d 11) d 12) d 13) b 14) a

15) b 16) c 17) a 18) c 19) a

www.OnlineIAS.com



ARITHMETIC

Under this heading we mainly deal with finding the day of the week on a particular givendate. The process of finding it lies in obtaining the number of odd days.

The number of days more than the complete number of weeks in a given period, arecalled odd days.

Leap & Ordinary Year. Every year which is divisible by 4 such as 1992, is called a leapyear. Every 4the century is a leap year but no other century is a leap year viz. 400, 800,1200, 1600 are all leap years, but none of 700, 900, 1100 etc. is a leap year.

An ordinary year has 365 days i.e.(52 weeks+1 day)A leap year has 366 days i.e.(52 weeks+2 days)An ordinary year has 1 odd day and a leap year has 2 odd days. A century i.e. 100

years has 76 ordinary years an 24 leap years.100 yers = 76 ordinary years + 26 leap years

= [(76.52) weeks + 76 days]+ (24.52) weeks + 48 days]= (5217 weeks + 5 days) = 5 odd days.

i.e. 100 years contain 5 odd days.200 years contain 10 and therefore 3 odd days.300 years contain 15 and there fore 1 odd day.400 years contain (20+1) and there fore 0 odd day.Similary, the years 800, 1200, 1600 etc. contain no odd day.We count days according to number of odd days.Sunday for 0 odd day, Monday for 1 odd day and so on.

EXERCISE1. Janurary 1, 1992 was a wednesday. What day of the week will it be on januray 1, 1993

a) Monday b) Tuesday c) Sunday d) Friday e) None2. On january 12, 1980, it was Saturday. The day of the week on January 12,1979 was:

a) Saturday b) Friday c) Sunday d) Thursday e) None3. On July, 2, 1985, it was Wednesday. The day of the week on july 2, 1984 was :

a) Wednesday b) Tues day c) Monday d) Thurs day e) None4. Monday falls on 4th April, 1988. What was the day on 3rd November, 1987 ?

a) Monday b) Sunday c) Tues day d) Wednesday e) None

16. CALENDARS

www.OnlineIAS.com



ARITHMETIC

5. Today is Friday. After 62 days it wiil be :a) Friday b) Thursday c) Saturday d) Monday e) None

6. Smt. Indira Gandhi died on 31st October, 1984. The day of the week was:a) Monday b) Tuesday c) Wednesday d) Friday e) None

7. The number of odd days in a leap year is:a) 1 b) 2 c) 3 d) 4 e) None

8. The year next to 1988 having the same calendar as that of 1988 is :a) 1990 b) 2001 c) 2002 d) 2003 e) None

9. The year next to 1991 having the same calendar as that of 1991 is :a) 1998 b) 2001 c) 2002 d) 2003 e) None

10. Today is 1st August. The day of the week is Monday. this is a leap year. the day of theweek on this day after 3 years will be :a) Wednesday b) Thursday c) Friday d) Saturday e) None

11. How many days are there from 2nd January 1993 to 15th March 1993:a) 72 b) 73 c) 74 d) 71 e) None

12. The first republic day of India was celebrated on 26th January, 1950. It was :a) Monday b) Tuesday c) Thursday d) Friday e) None

13. P.V. Narasimha Rao elected party leader on 29th May, 1991. What wasthe day of the week ?a) Tuesday b) Friday c) Wednesday d) Sunday e) None

ANSWERS OF CALENDARS :

1) d 2) b 3) c 4) c 5) b 6) c 7) b 8) c 9) c 10) b 11) b 12) c 13) c

www.OnlineIAS.com



ARITHMETIC

TRIANGLE1. Sum of any two sides is greater than the third side.2. Difference of any two sides is less than the third side.3. Sum of the three angles in triangle is 1800

Where b = base, h = height(attitude)

4. Area = bh2

1

5. Area = 2

4

3a for an equilateral triangle of side ‘a’

6. Height of equilateral triangle h = a23

7. Area of equilateral triangle =3

2h

8. Area = ))()(( csbsass

Where a, b and c are the sides and S =2

cba

RIGHT ANGLED TRIANGLE1. 222 bac

Where c = hypotenuse

2. Area = ab2

1 = half of the product of the sides with right angle.

CIRCLEwhere o = Centre

r = radiusd = diameter = 2r

1. Area = A = 2r =4

2d

2. circum ference = c = r2 = d

3. Ac 42

h

b

C

A

Ba

cb

r{ {

d

o

17. MENSURATION - TWO DIMENTIONAL

www.OnlineIAS.com



ARITHMETIC

SEMI CIRCLE

1. Area =82

22 dr

2. circumference = rr7

36)2(

SQUARE1. Four sides are equal2. Four angles are equal.(each angle is 900)

3. Area (A) =2

22 d

a

Where a = side, d = diagonal4. Perimiter P = 4a

5. Diagonal d = 2a

EXERCISE-1

1. The length and breadth of a room are 6 meters and 4 ½ meters respectively. Find floorarea of the room.a) 24 m2 b) 24 meter c) 27 meter d) 27 m2 e) None

2. If side square is 4 cm. find the length of its diagonal.a) 4 cm b) 4 2 cm c) 8 cm d) 16 cm e) None

3. Area of a square field is 729 square meter, find its perimeter.a) 27 meter b) 54 meter c) 81 meter d) 108 meter e) 58 meter

4. If diagonal of a square is 12 cm, find its area.

a) 36 cm2 b) 72 cm2 c) 144 cm2 d) 288 cm2 e) None

5. The area of a rhombus is 56 cm2. If length of one diagonal is 8 cm, find length of theother diagonal.

a) 7 cm b) 14 cm c) 15 cm d) 48 cm2 e) None

6. The length and breadth of a rectangle are 8 cm and 6 cm respectively. Find the length ofits diagonal.a) 5 cm b) 7 cm c) 10 cm d) 48 cm2 e) None

7. If the length of a rectangle is 8 cm and its diagonal is 10 cm, find its area.a) 64 cm2 b) 40 cm2 c) 48 cm2 d) 80 cm2 e) 89 cm2

ba

r

www.OnlineIAS.com



ARITHMETIC8. A man takes 15 minutes to walk along the diagonal of a square field at the rate of 2 km/

h. The area of the field is:a) 6250 m2 b) 12500 m2 c) 25000 m2 d) 50000 m2 e) None

9. Area of a square plot is 200 m2. Find the length of its diagonal.a) 20 meter b) 2 10 meter c) 10 meter d) 15 meter e) None

10. Find the area of a triangle whose base is 8 cm and height is 5 cm.a)13 cm2 b) 20 cm2 c) 40 cm2 d) 80 cm2 e) 75 cm2

11. The base of a triangle is 4/3 times its height. If area of the triangle is 600 cm2, find itsbase.a) 30 cm b) 40 cm c) 50 cm d) 60 cm e) 70 cm

12. The angles of a triangle are in the ratio of 3:4:5. What is degree of the smallest angle?a) 150 b) 300 c) 450 d) 600 e) 630

13. The base of a right angle triangle is 8 cm and hypotenuse is 10. Find its area.a) 12 cm2 b) 24 cm2 c) 40 cm2 d) 80 cm2 e) None

14. Two equal sides of a right isosceles triangle are 8 cm each. What is its area?a) 8 cm2 b) 16 cm2 c) 32 cm2 d) 64 cm2 e) None

15. If sides of a triangle are 8 cm, 15 cm and 17 cm respectively. Find its area.a) 60 cm2 b) 120 cm2 c) 240 cm2 d) 360 cm2 e) None

16. If diameter of a circle is 28 cm, then area of the circle is:a) 77 cm2 b) 154 cm2 c) 308 cm2 d) 616 cm2 e) None

17. Two parallel sides of a trapezium are 4 cm and 5 cm respectively. The perpendiculardistance between the parallel sides is 6 cm. Find the area of the trapezium.a) 27 cm2 b) 30 cm2 c) 40 cm2 d) 54 cm2 e) None

18. In a quadrilateral, length of one diagonal is 15 cm and the lengths to the perpendicularsdrawn from the opposite vertices are 7 cm and 9 cm. Find the area of the quadrilateral.a) 30 cm2 b) 60 cm2 c) 90 cm2 d) 120 cm2 e) None

19. If circumferance of a circle is 88 cm. Find radius of the circle.a) 7 cm b) 14 cm c) 22 cm d) 44 cm e) None

20. If area of a circle is 154 cm2, find its radius.a) 7 cm b) 14 cm c) 21 cm d) 28 cm e) None

21. The length and breadth of a rectangle are in the ratio of 5:3. If area of the rectangle is60cm2, find its length.a) 2 cm b) 5 cm c) 6 cm d) 10 cm e) None

22. The length and breadth of a rectangle are in the ratio of 5:3. Find its area, if the perimeteris 64 cm.a) 15 cm2 b) 60 cm2 c) 150 cm2 d) 240 cm2 e) None

23. Area of a rectangle plot is 1200m2. Find the perimeter of the plot if its length and breadthare in the ratio of 4:3.

a) 127 meter b) 154 meter c) 140 meter d) 108 meter e) 158 meter

24. The cost of flooring a plot at the rate of Rs. 50 per meter is Rs. 30000. If ratio of length andbreath of the plot is 3:2, find the cost of fencing at the rate of Rs. 25 per meter.


www.OnlineIAS.com



ARITHMETIC25. The cost of carpeting a hall at Rs. 30 per square meter is Rs. 5400. Had the length been

4 meter less, the cost would have been Rs. 3960. Find the breadth of the hall.

a) 12m b) 14 m c) 15 m d) 16 m e) None

26. Perimeter of a rectangle is 28 cm and its area is 48 sq. cm. Find length of its diagonal.

a) 10 cm b) 5 cm c) 5 2 d) 10 e) None27. If a perimeter and area of a square are equal. Side of the square(in cm) is:

a) 4 cm b) 5 cm c) 6 cm d) 10 cm e) None28. The diameter of a wheel is 14 cm. How many revolutions the wheel is required to make,

to cover a distance of 880 cm?a) 10 b) 20 c) 25 d) 40 e) 50

29. How many revolutions are required to be made by a wheel of 42 cm in diameter to coverthe same distance as covered by a wheel of 49 cm in radius in 18 revolutions?a) 21 b) 42 c) 49 d) 84 e) None

30. The diameter of the wheel of a vehicle is 5 meter. It makes 7 revolutions per 9 seconds.What is speed of the vehicle in km/h?a) 30 km/h b) 36 km/h c) 40 km/h d) 44 km/h e) None

31. The perimeter of a rhombus is 60 cm and one of its diagonal is 24 cm. Find length of theother diagonal of the rhombus.a) 12 cm b) 18 cm c) 24 cm d) 36 cm e) None

32. If side and diagonal of a rhombus are 5 cm and 8 cm respectively. Find area of therhombus.a) 20 cm2 b) 24 cm2 c) 40 cm2 d) 48 cm2 e) None

33. If all the sides of a square are doubled. Ratio of the area of new square and that of theoriginal square is:a) 1:1 b) 2:1 c) 4:1 d) 3:4 e) Data sufficient

34. The radius of a circle is 7 cm. Find the radius of another circle whose area is 25 times ofarea of the first circle.a) 5 cm b) 32 cm c) 35 cm d) 172 cm e) None

35. A field is 40 meter long and 35 meter wide. The field is surrounded by a path of uniformwidth of 2.5 meter runs round it on the outside. Find the area of the path.a) 250 m2 b) 400 m2 c) 500 m2 d) 600 m2 e) 800 m2

36. A field is 100 meter long and 60 meter wide. A path of uniform width of 5 meter runs roundit on the inside. Find the area of the path.

a) 200 m2 b) 400 m2 c) 800 m2 d) 1500 m2 e) 1600 m2

37. Find area of uniform path of width 2 meter running from center of each side to the oppositeside of a rectangle field measuring 17 meter by 12 meter.

a) 24 m2 b) 34 m2 c) 48 m2 d) 54 m2 e) None

www.OnlineIAS.com



ARITHMETIC38. If length of a rectangle is increased by 50%, by what percent should its width be decreased

to get the same area as before?

a) 25% b) 33.33% c) 50% d) 100% e) 34.23%

39. If length of a rectangle is reduced by 20% and width remaining the same. Area of theresulting rectangle will be decreased by:

a) 10% b) 20% c) 25% d) 40% e) None

40. If length of a rectangle is decreased by 20%, buy what percent should its width beincreased to get the same area as before?

a) 16.67% b) 20% c) 25% d) 30% e) None

41. If the length of a rectangle is increased by 30% and width by 20%, its area will increaseby:

a) 50% b) 25% c) 56% d) 60% e) None

42. If all the sides of a square are increased by 20%, its area is increased by:

a) 4% b) 20% c) 40% d) 44% e) None

43. If all the sides of a square are increased by 200%, its area is increased by:

a) 200% b) 400% c) 600% d) 800% e) None

44. If radius of a circle is increased by 105. Area of the resulting circle will be increased by:

a) 11% b) 20% c) 21% d) 25% e) None

45. If all the sides of a square are decreased by 10%, its area will be decreased by:

a) 19% b) 20% c) 21% d) 22% e) None

46. If length of a rectangle is increased by 10% and width; is decreased by 10%, its areawill:

a) 20% increase b) 1% decrease c) 20% decrease d) 2% decrease e) Remains unchanged

47. If length of a rectangle is decreased by 20% and width by 30%m, its area will decreaseby:

a) 44% b) 50% c) 56% d) 60% e) None

www.OnlineIAS.com



ARITHMETIC48. A towel was 40 cm broad and 90 cm long. When bleached, it was found to have lost 20%

of its length and 10% of its width. The percentage decrease in area is:

a) 28% b) 30% c) 32% d) 33% e) 35%

49. A square and a rectangle each has perimeter 60 metre. Difference between the areas ofthe two figures is 16 square metre. Find length of the rectangle.

a) 12m b) 14 m c) 15 m d) 16 m e) 19 m

50. Find the radius of a circle whose area is equal to the sum of areas of three circles withradii 8cm, 9cm, 12cm respectively.

a) 5 cm b) 32 cm c) 35 cm d) 17 cm e) None

51. If difference between circumference and diameter of a circle is 30 cm, find radius of thecircle.

a) 7 cm b) 3 cm c) 5 cm d) 19 cm e) 20 cm

52. A uniform path of 7 metre surrounds a circular field whose diameter is 42 metre. Find thearea of the path.

a) 1024 m2 b) 1234 m2 c) 1448 m2 d) 1554 m2 e) 1078 m2

53. The area of the ring between two concentric circles, whose circumferences are 88 cmand 132 cm is

a) 720 cm2 b) 724 cm2 c) 740 cm2 d) 748 cm2 e) 770 cm2

54. Two poles whose heights are 11 metre and 5 metre stand upright in a field. If the distancebetween their feet is 8 metre, what is the distance between their tops?

a) 12m b) 14 m c) 10 m d) 16 m e) 19 m

55. What will be the cost of fencing a square field, whose side is 20 metre, if the cost offencing is Rs. 10 per meter?


56. How many tiles of 20cmx5cm are required for paving the floor of a room 25 metre long and10 metre wide?

a) 25 b) 250 c) 25000 d) 2500 e) None

www.OnlineIAS.com



ARITHMETIC57. The length and breadth of a room is 15 metre and 8 metre respectively. Find the length of

3 metre wide carpet required to cover the floor of the room.

a) 42m b) 54 m c) 40 m d) 56 m e) 19 m

58. Find the area of the largest circle that can be inscribed in a square of 14 cm, a side.


59. The radius of a circle is 5 cm. What is the ratio between its area and circumference?

a) 2:5 b) 5:2 c) 2:3 d) 3:2 e) None

60. The radius of a circle is 10 cm. What percentage the area of circle is of its circumference?

a) 500% b) 502% c) 900% d) 800% e) None

61. The area of a circle and its circumference are equal, find its diameter.

a) 2cm b) 5 cm c) 12 cm d) 6 cm e) 4 cm

62. Between a square of perimeter 44 cm and a circle of circumference 44cm, which figurehas larger area and by how much?

a) Circle 33 cm2 b) Square154 cm2 c) Circle 140 cm2 d) Square 148 cm2 e) None

63. A horse is tied to one of the corners of a square field whose side is 20 metre. If length ofthe rope is 14 metre, find the area of ungrazed field.

a) 246 m2 b) 234 m2 c) 448 m2 d) 554 m2 e) 78 m2

64. 4 horses are tied-one to each corner of a square with 14 m a side, and length of the ropeis 7m. Find the area of ungrazed field.

a) 46 m2 b) 34 m2 c) 48 m2 d) 54 m2 e) 42 m2

65. The circumference of two circle are 176 metre and 132 metre respectively. What is thedifference between their radii?

a) 8m b) 5 m c) 4 m d) 6 m e) 7 m

66. A wire is bent into the shape of a square, encloses an area of 81 cm2. If the wire is bentinto a semicircular shape, find its area.a) 77 cm2 b) 54 cm2 c) 14 cm2 d) 18 cm2 e) None

www.OnlineIAS.com



ARITHMETIC67. A wire, bent in the form of a square, encloses an area of 484 cm2. If the same wire is bent

so as to form a circle, then area of the circle is:a) 77 cm2 b) 54 cm2 c) 14 cm2 d) 18 cm2 e) 616 cm2

68. The parallel sides of a trapezium are 15 cm and 29 cm. If the non-parallel sides are 13 cmand 15 cm, what is the area of trapezium?a) 277 cm2 b) 264 cm2 c) 214 cm2 d) 218 cm2 e) 616 cm2

69. In a parallelogram two adjacent sides are 33 cm and 56 cm and one diagonal is 65 cm.What is its area?a) 1277 cm2 b) 1264 cm2 c) 1848 cm2 d) 1218 cm2 e) 1616 cm2

ANSWERS FOR MENSURATION-TWO DIMENTIONALEXERCISE

1) d 2) b 3) d 4) b 5) b 6) c 7) c 8) e 9) a 10) b 11) b 12) c 13) b 14) c

15) a 16) d 17) a 18) d 19) b 20) a 21) d 22) d 23) c 24) d 25) a 26) d 27) a 28) b

29) b 30) 31) b 32) b 33) c 34) c 35) b 36) d 37) d 38) b 39) b 40) c 41) c 42) d

43) d 44) c 45) a 46) b 47) a 48) a 49) e 50) d 51) a 52) e 53) e 54) c 55) d 56) c

57) c 58) b 59) b 60) a 61) e 62) a 63) a 64) e 65) e 66) a 67) e 68) b 69) c

www.OnlineIAS.com



ARITHMETIC

Three dimensional figures: Three-dimensional figures have three dimensions viz. length,breadth and height.

Surface Area : Total of surface areas of each side of the figure. It is always measured insquare units.

Volume : Space occupied by the object is called its volume. It is always measured incube units.

An object having length, breadth and height (thickness) is called a solid. The side portions of

a solid are called lateral surfaces.

Cube1. Volume of the cube 3a Cubic Unitss

2. Whole surface are of the cube 26a Sq. Units

3. Four walls area of the cube 24a4. Diagonal of a cube 3a Units

Cuboid1. Volume of a cuboid = l b h cubic unitss2. Whole surface area of cuboid = 2(lb+bh+lh) Sq. Units

3. Four walls area of the cube 2 ( )h l b

4. Diagonal of a cuboid 2 2 2l b h Unitswhere l = length, b = breadth, h = height

Cylinder1. Volume of the cylinder 2r h Cu.Unitss

2. Curved surface area of the cylinder 2 rh Sq.Units

3. Total surface area of the cylinder 2 2 ( )2 2 r h rrh r Sq.Unitss

Where r = radius of the base, h = heightSphere

1. Volume of the sphere 343r

18. MENSURATION-THREE DIMENTIONAL{ r

www.OnlineIAS.com



ARITHMETIC

2. Surface area of the sphere 24 r Sq.Units

3. Volume of a hemisphere 323r Cu.Unitss

4. Curved surface area of the hemisphere 22 r Sq.Units

5. Whole surface area of the hemisphere 23 rCone

1. Slant height 2 2h rl

2. Volume of the cone 213r h Cu.Unitss

3. Curved surface area of the cone rl Sq.Units 2 2h rr Sq.Units

4. Total surface area of the cone 2 ( )r l rrl r Sq.Unitss

Exercise1. Find the total surface area of a hemisphere of radius of 7 cm.


2. Find the curved surface area of a hemisphere whose diameter is 14cm.


3. Find the volume of air in a room whose floor area is 40 m2 and the height is 5 meter.

a) 8 m3 b) 100 m3 c) 200 m3 d) 400 m3 e) 350 m3

4. Find the height of a cuboids whose volume and base area are 144 m3 and 18 m2

respectively.

a) 6 meter b) 7 meter c) 7 ½ meter d) 8 meter e) None

r

lh

www.OnlineIAS.com



ARITHMETIC5. Find the length of longest pole that can be placed in a room 12 meter long, 8 meter

broad and 9 meter high.


6. The length, breadth and height of a room are 7 meter, 6 meter respectively. Find thearea of four walls.

a) 130 m2 b) 144 m2 c) 154 m2 d) 210 m2 e) None

7. The surface area of a cube is 486 m2. Find its volume.


8. The areas of three adjacent sides of a cuboids are 15 m2, 12 m2 and 5 m2. What is thevolume of the cuboid?

a) 30 m3 b) 60 m3 c) 180 m3 d) 75 m3 e) None

9. If each side of a cube is increased by 30%, then its surface area will be increased by:

a) 50% b) 51% c) 60% d) 69% e) None

10. If radius and height of a cylinder are increased by 20%, find percentage increase in itsvolume.

a) 40% b) 44% c) 66% d) 72.8 % e) None

11. Dimensions of a cuboid are 29 cm, 18 cm and 15 cm. If its sides are increased by20%, 25% and 40% respectively, find percent increase in its volume.

a) 85% b) 104% c) 110% d) 121% e) None

12. Two cubes each 6 m edge are joined end to end. The surface area of the resultingcuboid is:


13. If ratio of radii of two cylinders is 2:3 and ratio of their heights is 5:4, find the ratio oftheir volumes.

a) 8:27 b) 25:16 c) 5:6 d) 5:9 e) None

14. A pipe of diameter d can drain a certain water tank in 40 minutes. The time taken by apipe of diameter 2d for doing the same job is:


15. The diameter and height of a cone are 14 cm and 24 cm respectively. Find curvedsurface area of the cone.


www.OnlineIAS.com



ARITHMETIC16. The length, breadth; and height of a room are 5 meter and 4 meter and 4 meter

respectively. If all the four walls of the room are to be coveted with 50 cm wide wallpaper, find the length of the paper required.


17. A square card board has a side 10 cm. From each corner a square of 3 cm is cut downand then the corners are folded to make an open box. What is the volume of open box?


18. Volume of two spheres is in the ratio of 27:125. Find radius of the bigger sphere, ifradius of smaller sphere is 27cm.


19. Volume of two spheres is in the ratio 343:8. Find the ratio between their surface areas.

a) 7:2 b) 49:4 c) 81:45 d) 343:8 e) None

20. Three solid cubes whose sides are 3 cm, 4 cm and 5 cm respectively are melted to forminto a single cube. Find the side of new cube formed.


21. How many cubes of 2 cm, a side can be made by melting a solid cube of 6 cm, a side?

a) 8 b) 9 c) 27 d) 216 e) None

22. Find the cost of canvas cloth required for conical tent whose height is 3 m and radius is4 m and cost of cloth is Rs. 140 per square meter.


23. How many spheres of diameter 2 cm can be made by melting one sphere of radius4cm?

a) 16 b) 32 c) 64 d) 128 e) 256

24. A well 2 meter in radius has been dug 5 meter deep and the earth taken out was spreadto make an embankment 1 meter wide round the well. What is the height of theembankment?


25. A cube of 9 cm a side is melted and 27 small cubes are made from that. Find side ofthe smaller cubes.

a) 1.5 cm b) 2 cm c) 2.5 cm d) 3 cm e) None

26. A box is made of 1 cm thick wood. If outer dimensions of box are 12 cm by 10 cm by 7cm find the volume of wood used.


www.OnlineIAS.com



ARITHMETIC

27. A wooden box without lid has external length, breadth and height 11 cm, 9 cm and 7cm respectively. If wood is 5 mm thick, find the volume of wood used in making thebox.


28. How much metal is required to make a 20 meter ling pipe, if its inner and outerdiameter are 6 meter and 8 meter respectively.

a) 300 m3 b) 600 m3 c) 180 m3 d) 750m3 e) None

29. A sphere of radius 3 cm is put into water contained in a cylinder of 6 cm radius. If thesphere is completely immersed in the water, the water level in the cylinder rises by:

a) 1 cm b) 1/3 cm c) ½ cm d) 2/3 cm e) None

30. How many solid spherical balls of radius 3 cm each are required to immerse in acylinder jar of radius 4 cm to raise the level of water in the jar by 9 cm?

a) 4 b) 6 c) 9 d) 16 e) None

31. A wire is drawn from a slid iron sphere of radius 6 cm. Find the length os the wire, ifits diameter is 6 cm.


32. A solid cylinder of metal, whose radius is 6 cm and height is 125 cm is melted into asphere, Find the radius of the sphere.


33. A well 2 meter in radius has been dug 5 meter deep and the earth taken out wasspread to make an embankment 1 meter wide round the well. What is the height ofthe embankment?


ANSWERS FOR THREE DIMENTIONALEXERCISE

1) c 2) b 3) c 4) d 5) b 6) a 7) d 8) a 9) d 10) d 11) c 12) b 13) d 14) a

15) c 16) c 17) b 18) a 19) b 20) a 21) c 22) b 23) c 24) b 25) d 26) a 27) a 28) e

29) a 30) a 31) b 32) d 33) b

www.OnlineIAS.com



...4. A number is divisible by 5. If the last digit is either ‘0’ or ‘5’. 5. A number is...

Documents

Transcript of ...4. A number is divisible by 5. If the last digit is either ‘0’ or ‘5’. 5. A number is...