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2 IBPS BANK PO EXAM 2013 : Quantitative Aptitude

Table of Contents

PREFACE ............................................................................................................................................. 6

IMPORTANT CHAPTER GUIDELINES ........................ ........................... ......................... ............... 7

CHAPTER: SIMPLIFICATION & APPROXIMAITON ................................................................... 8

Solved Examples (Simplification & Approximation) ............................................................................................. 12

Practice Set-1 (Simplification & Approximation) .................................................................................................. 22

Practice Set-2 (Simplification & Approximaiton) .................................................................................................. 25

Simplification & Approximaiton Averages Practice Set-1 (Answers) .................................................................... 27

Simplification & Approximaiton Averages Practice Set-2 (Answers) .................................................................... 28

CHAPTER: NUMBER SERIES ....................... .......................... ......................... ........................... .... 29

Solved Examples (Number Series) ........................................................................................................................ 33

Practice Set (Number Series)................................................................................................................................ 38

Number Series Practice Set (Answers) ................................................................................................................. 41

CHAPTER: NUMBER SYSTEM .......................... .......................... ......................... ......................... . 42

Solved Examples (Number System) ...................................................................................................................... 48

Practice Set-1 (Number System) .......................................................................................................................... 53

Practice Set-2 (Number System) .......................................................................................................................... 55

Number System Practice Set-1 (Answers) ............................................................................................................ 58

Number System Practice Set-2 (Answers) ............................................................................................................ 59

CHAPTER: RATIO, PROPORTION & ALLIGATION ........................................ ......................... . 60

Solved Examples (Ratio, Proportion & Alligation) ................................................................................................ 66

Practice Set-1 (Ratio, Proportion & Alligation) ..................................................................................................... 70

Practice Set-2 (Ratio, Proportion & Alligation) ..................................................................................................... 74


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Ratio, Proportion & Alligation Practice Set-1 (Answers) ....................................................................................... 77

Ratio, Proportion & Alligation Practice Set-2 (Answers) ....................................................................................... 78

CHAPTER: AVERAGES ................................................................................................................... 79

Solved Examples (Averages) ................................................................................................................................ 80

Practice Set (Averages) ........................................................................................................................................ 86

Averages Practice Set (Answers) .......................................................................................................................... 90

CHAPTER: PERCENTAGES, PARTNERSHIP AND SHARE .......................................... ............. 91

Solved Examples (Percentages, Partnership and Share) ....................................................................................... 95

Practice Set-1 (Percentages, Partnership and Share) .......................................................................................... 101

Practice Set-2 (Percentages, Partnership and Share) .......................................................................................... 104

Percentages, Partnership and Share Practice Set-1 (Answers) ........................................................................... 106

Percentages, Partnership and Share Practice Set-2 (Answers) ........................................................................... 107

CHAPTER: PROFIT & LOSS ........................................................................................................ 108

Solved Examples (Profit & Loss) ......................................................................................................................... 112

Practice Set (Profit & Loss) ................................................................................................................................. 117

Profit & Loss Practice Set (Answers) .................................................................................................................. 121

CHAPTER: SIMPLE INTEREST & COMPOUND INTEREST ................................ .................. 122

Solved Examples (Simple Interest & Compound Interest) .................................................................................. 126

Practice Set (Simple Interest & Compound Interest) .......................................................................................... 132

Simple Interest & Compound Interest Practice Set (Answers) ............................................................................ 136

CHAPTER: TIME AND WORK .................................................................................................... 137

Solved Examples (Time and Work) ..................................................................................................................... 140

Practice Set (Time and Work)............................................................................................................................. 146

Averages Practice Set (Time and Work) ............................................................................................................. 151


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CHAPTER: SPEED DISTANCE & TIME ..................................................................................... 152

Solved Examples (Speed Distance & Time)......................................................................................................... 156

Practice Set (Speed Distance & Time) ................................................................................................................ 162

Speed Distance & Time Practice Set (Answers) .................................................................................................. 166

CHAPTER: MENSURATION ........................................................................................................ 167

Solved Examples (Mensuration) ........................................................................................................................ 174

Practice Set (Mensuration) ................................................................................................................................ 178

Mensuration Practice Set (Answers) .................................................................................................................. 181

CHAPTER: PERMUTATIONS, COMBINATIONS & PROBABILITY ..................................... 182

Solved Examples (Permutations, Combinations & Probability) .......................................................................... 188

Practice Set-1 (Permutations, Combinations & Probability) ............................................................................... 195

Practice Set-2 (Permutations, Combinations & Probability) ............................................................................... 197

Permutations, Combinations & Probability Practice Set-1 (Answers) ................................................................. 199

Permutations, Combinations & Probability Practice Set-2 (Answers) ................................................................. 200

CHAPTER: DATA INTERPRETATION ...................................................................................... 201

CHAPTER: DATA INTERPRETATION-TABLE CHART ......................................................... 204

Solved Examples (Data Interpretation-Table Chart) ........................................................................................... 206

Practice Set (Data Interpretation-Table Chart) ................................................................................................... 213

Data Interpretation-Table Chart Practice Set (Answers) .................................................................................... 221

CHAPTER: DATA INTERPRETATION-LINE GRAPHS ........................ ......................... .......... 222

Solved Examples (Data Interpretation-Line Graphs) .......................................................................................... 225

Practice Set (Data Interpretation-Line Graphs) .................................................................................................. 229

Data Interpretation-Line Graphs Practice Set (Answers) .................................................................................... 233

CHAPTER: DATA INTERPRETATION-BAR GRAPHS ......................... ......................... .......... 234


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Solved Examples (Data Interpretation-Bar Graphs)............................................................................................ 237

Practice Set (Data Interpretation-Bar Graphs) ................................................................................................... 243

Data Interpretation-Bar Graphs Practice Set (Answers) ..................................................................................... 247

CHAPTER: DATA INTERPRETATION-PIE DIAGRAM .......................................................... 248

Solved Examples (Data Interpretation-Pie Diagram) .......................................................................................... 250

Practice Set (Data Interpretation-Pie Diagram) .................................................................................................. 256

Data Interpretation- Pie Diagram Practice Set (Answers) ................................................................................... 262

CHAPTER: DATA INTERPRETATION-CASE LETS ................................................................ 263

Solved Examples (Data Interpretation-Caselets) ................................................................................................ 266

PracticeSet-(Data Interpretation- Caselets)........................................................................................................ 270

Data Interpretation-Caselets Practice Set (Answers).......................................................................................... 274

Solved Examples (Data Interpretation-Miscellaneous) ...................................................................................... 275

Practice Set (Data Interpretation-Miscellaneous) .............................................................................................. 285

Data Interpretation-Miscellaneous Practice Set (Answers) ................................................................................ 291

FEEDBACK ..................................................................................................................................... 292


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Preface

Jagranjosh’s IBPS PO Exam 2013: Quantitative Aptitude e-Book is a one-stop solution for aspirants who

endeavor to leave no stone unturned to score considerably in IBPS PO Written Examination 2013. The

eBook is highly useful for all officers level Banking exams - IBPS Specialist officers Exam and SBI PO

Exam.

IBPS PO Exam 2013: Quantitative Aptitude e-Book is prepared by Jagranjosh’s team of subject matter

experts who worked up the best to come up with this all-inclusive preparation package for Quantitative

Aptitude section of Officers level Banking Exams. This eBook is a perfect blend of chapter-wise basic

concepts and questions regarding all the units included in the syllabus for Quantitative Aptitude Section

of Officers level Banking Exams. The chapter-wise compilation of this e-Book makes the concept of

Quantitative aptitudes easy to understand for students. It further includes previous year questions andmodel practice sets along with the importance factor of each and every chapter included out here.

Our IBPS PO Exam 2013: Quantitative Aptitude e-Book will let students to practice for the QA section

within the standard time limit set by the IBPS examination board. This will help them hone ‘time

management’ skills.

The IBPS PO Exam 2013: Quantitative Aptitude e-Book includes:

• Chapter wise Basic Concepts & Questions

• IBPS PO Previous Year Questions

• Chapter wise Model Practice Set

• Important Chapter Guidelines

Jagranjosh’s IBPS PO Exam 2013: Quantitative Aptitude e-Book is a one-stop solution edition to help

preparing for the QA Section of Officers level Banking Exams. All the chapters of this e-book are reader-

friendly and easy to understand. Just prepare with it to score more.

Our team at Jagranjosh.com wishes all the very best to the aspirants of Banking Exams.

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Important Chapter Guidelines

Important Chapter Guidelines for IBPS PO 2013 : Quantitative Aptitude

Chapter Importance

Number System Very Important

Number Series Very Important

Percentage Partnership and Share Very Important

Simplification and Approximation Very Important

Average Important

Ratio ,Proportion & Alligation Important

Time & Work Important

Profit, Loss & Discount Very Important

Simple Interest and Compound Interest Important

Time, Distance and Speed Important

Permutation and Combination & Probability Very Important

Data Interpretation-Table Charts Very Important

Data Interpretation-Bar Graph Very Important

Data Interpretation-Line Graph Very Important

Data Interpretation-Pie Charts Very Important

Data Interpretation-Caselets Very Important

Data Interpretation-Miscelleneous Graphs Very Important

Mensuration Important

Note : Prepared on the basis of questions asked in previous year papers


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Chapter: Simplification & Approximaiton Some Important Concepts

‘BODMAS’ Rule: This ‘BODMAS’ Rule shows the correct sequence of all the operations that are

to be executed to find out the value of a given expression. In this rule ‘B’ Stands for ‘Bracket’,

‘O’ stands for ‘of’, ‘D’ for ‘Division’, ‘M’ for ‘Multiplication’, ‘A’ for ‘Addition’ and ‘S’ for

‘Subtraction’.

Therefore, the correct order to simplify an expression is:

(a) ( )(b) {}(c) [](d) of(e) Division(f) Multiplication(g) Addition(h) SubtractionModulus of a Real Number: If the real number is ‘r’, then

| r | = .

Example: What will be the value of x in the following equation?

5 + + x +2 = 9 .

Solution: Simplifying the above equation

x = 9 - 5 - – 2 x = - - -

x =

x = = 1 .


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Approximation

In these types of questions there is no need to find out the exact values. The candidate is

required to calculate the approximate value in the following manner:

Step I: Round off the numbers given in the question.

Step II: Simplify the value

Step III: Round off the final simplified value

Rounding off numbers:

Rounding off the numbers given in the question can be done in the following manner:

(a) Rounding off to the nearest 10:Example: Rounded off value of 56 is 60, because the digit at unit place is greater than 5,

therefore, we will add 1 to the digit at tens place and replace the unit’s digit by 0.

Example: Rounded off value of 54 is 50, because the digit at unit place is less than 5,

therefore, the value at tens place will remains the same and unit’s digit will be replaced

by 0.

Example: Rounded off value of 35 is 40, because the digit at unit place is equal to 5,

therefore, we will add 1 to the digit at tens place and replace the unit’s digit by 0.

(b) Rounding off to the nearest 100:Example: Rounded off value of 386 is 400, because the digit at tens place is greater than

5, therefore, we will add 1 to the digit at hundreds place and replace the digit at unit

and tens places by 00.

Example: Rounded off value of 741 is 700, because the digit at tens place is less than 5,

therefore, the value at hundreds place will remains the same. Unit and tens digit will be

replaced by 00.

(c) Rounding off to the nearest 1000Example: Rounded off value of 1963 is 2000, because the digit at hundreds place is

greater than 5, therefore, we will add 1 to the digit at thousand place and replace the

ones, tens and hundreds by 000.

Although the numbers can be rounded off by the above procedures but it depends on the other

numbers involved in the simplification.

Rounding off a number to a decimal place:


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The candidate is required to follow the following steps to round off a number to the nth

decimal place:

Step I: check the digit immediately, next right to the nth place.

Step II: Add 1 to the digit in the nth place, if the next right digit is 5 or more, otherwise the digit

will remains the same.

Step III: Remove all the digits in places to the right of the nth place.

Example: Rounded off value of 4.693 to the second place is 4.69, because next right digit to the

second place is 3, therefore, the value will remain the same and the digit in place to the right of

the second place will be removed.


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Solved Examples (Simplification & Approximation)

Directions (1-5) What will come in place of the question mark (?) in the following question?

(IBPS PO/MT Exam 2012)

1. 4003 × 77 - 21015=? × 116

(1) 2477

(2) 2478

(3) 2467

(4) 2476

(5) None of these

Solution: ? × 116 = 4003 × 77 – 21015

or, ? × 116 = 308231 – 21015 = 287216

or, ? × 116 = 287216

? = = 2476

Ans: (4)

2.

(1) 143

(2)

(3) 134

(4)

(5) None of these

Solution:

=- 361

= - 361

= 504 -361 = 143

Ans: (1)


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3. (4444÷40) + (645÷25) + (3991÷26) =?

(1) 280.4

(2) 290.4(3) 295.4

(4) 285.4

(5) None of these

Solution: (4444÷40) + (645÷25) + (3991÷26)

= + +

= 111.1 + 25.8 + 153.5 = 290.4

Ans: (2)

4. × - (83)2

= (?)2 + (37)

2

(1) 37

(2) 33

(3) 34

(4) 38

(5) None of these

Solution: (?)2

+ (37)2 = × - (83)

2

or, (?)2 + (37)

2 = 182×51 - (83)

2

or, (?)2 + 1369 = 9282-6889 =2393

or, (?)2 = 2393 - 1369 = 1024

?= = 32

Ans: (5)

5. 5 × 4 × 11 + 2 =?

(1) 303.75

(2) 305.75

(3)

(4)

(5) None of these


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Solution: ? = 5 × 4 × 11 + 2

= × × +

= × × +

= 101× 3 + = 303 + =

= = 305.75

Ans: (2)

Direction (6-10): What approximate value should come in place of the question mark (?) in

the following question? (Note: You are not excepted to calculate the exact value.)


6. 8787 ÷ 343 × =?

(1) 250

(2) 140

(3) 180

(4) 100(5) 280

Solution: ? = 8787 ÷ 343 ×

= 25.61 × 7.07 = 181.09

Ans: (3)

7. × (303÷8) = (?)2

(1) 48(2) 38

(3) 28

(4) 18

(5) 58

Solution: × (303÷8) = (?)2


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or, 38 × 37.8 = (?)2 (37.8 ~ 38)

or, 38 × 38 = (?)2

Ans: (2)

8. of 4011.33 + of 3411.22 =?

(1) 4810

(2) 4980

(3) 4890

(4) 4930

(5) 4850

Solution: ? = 4011.33 + 3411.22

= +

= 2507.08 + 2387.854 = 2507 + 2387

= 4894

Ans: (3)

9. 23% of 6783 + 57% of 8431=?

(1) 6460

(2) 6420

(3) 6320

(4) 6630

(5) 6360

Solution: ?= 23% of 6783 + 57% of 8431

6783 + 8431

= 23

= 1560.09 + 4805.67 = 6365.76

Ans: (5)


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10. 335.01 × 244.99÷55=?

(1) 1490

(2) 1550(3) 1420

(4) 1590

(5) 1400

Solution: ? = 335.01 × 244.99 55

= 335 × 245 55

= 335 × = = 1422.27 1490

Ans: (1)

Directions (Q.11-15): What will come in place of the question mark (?) in the following

questions?


11. 3463 × 295 - 18611 =? + 5883

(1) 997091

(2) 997071

(3) 997090

(4) 999070

(5) None of these

Solution: 3463 x 295 -18611 =? + 5883

? = 1021585 - 18611 - 5883 = 997091

Ans: (1)


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12. (23.1)2 + (48.6)

2 - (39.8)

2 =? + 1147.69

(1) (13.6)2

(2)

(3) 163.84

(4) 12.8

(5) None of these

Solution: 533.61 + 2361.96 - 1584.04 =? + 1147.69

or, ? = 1311.53 - 1147.69 = 163.84

Ans: (3)

13. + = ?

1)

2) 0.75

3) 1

4) None of these

Solution: + = = = =

Ans: (4)


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14. [(3 + ) X (8 + 7 )]- 98 =?

(1) 2

(2) 8

(3) 382

(4) 386

(5) None of these

Solution: [ (3 +1) (8 + 7) ]- 98

= [4 15 ] - 98

= [60 8] - 98 = 480 - 98 = 382

Ans: (3)

15. - (54)2 = + (74)

2

(1) 3844

(2) 3721

(3) 3481

(4) 3638

(5) None of these

Solution: - (54)2

- (74)2

=

or , = - 2916 - 5476

= 8453 - 2916 - 5476 = 61


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or , ? = (61)2 = 3721

Ans: (2)

Directions ( 16-20): What approximate value should come in place of question mark (?) in the

following questions?

(Note: You are not expected to calculate the exact value] (IBPS PO/MT Exam 2011)

16. 39.897% of 4331 + 58.779% of 5003 =?

(1) 4300

(2) 4500

(3) 4700

(4) 4900

(5) 5100

Solution: 40 + 59 = 1732 + 2950 = 4682 4700

Ans: (3)

17. 43931.03 / 2111.02 x 401.04 =?

1) 8800

2) 7600

3) 7400

4) 9000

5) 8300

Solution: 43931 2111 401 =?

or, ? = 44000 400


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or, ? = 400 = 8800

Ans: (5)

18. 34.993 =?

1) 3000

2) 2800

3) 2500

4) 3300

5) 2600

Solution: 34.993 = 80 x 35 = 2800

Ans: (2)

19. +349 =? 21.003

1) 7600

2) 7650

3) 7860

4) 7560

5) 7680

Solution: 17 + 349 =? 21

or, 366 21 = ?

or, ? = 7686 7680.

Ans: (5)


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20. 59.88 12.21 6.35 =?

1) 10

2) 50

3) 30

4) 70

5) 90

Solution: 60 12 6 = 30

Ans: (3)


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Practice Set-1 (Simplification & Approximation)

Directions (Q. 1-5): What will come in place

of question mark (?) in the following

questions? (IBPS RRB Grade A Officer Exam

2012)

1.

(1) (2) 2(3) 16(4) 8(5) None of these2. 55% of

(1) 126.5(2) 126.6(3) 124.6(4) 125.4(5) None of these3.

(1) (2) (3)

(4) 18(5) 324.

(1) 81

(2) 64(3) –8(4) –7(5) 95.

(1) 6(2) 2(3) 4(4) 0(5) None of theseDirections (Q. 6-10). What approximate

value will come in place of question mark

(?) in the following questions? (You are not

expected to calculate the exact value.)

6. 68% of 1288 + 26% of 734 – 215 =?

(1) 620(2) 930(3) 540(4) 850(5) 7107.

(1) 670(2) 530(3) 420(4) 780(5) 960

8. 6578 ÷ 67 15 =? 6


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(1) 200(2) 250(3) 150(4) 100(5) 3009.

(1) 540(2) 760(3) 800(4) 1260(5) 104010.

(1) 840(2) 910(3) 1320(4) 1120(5) 1550Directions (Q.11 to 15): What will come in

place of question mark (?) in the following

questions? (RBI Grade ‘B’ Officers Exam

2011)

11. [(3024 ÷ 189)1/2 + (684 ÷ 19)2] = (?)2 +

459

(1) -27(2) -29(3) 31(4) 841(5) 108912. 4.4 times of 30% of 216 =?

(1) 81.9(2) 83.7(3) 87.3(4) 89.1

(5) None of these13. (0.0729 ÷ 0.1)

3 ÷ (0.081 × 10)

5 × (0.3 ×

3)5 = (0.9)? + 3

(1) 1(2) 2(3) 4(4) 7(5) None of these14. of × 5) = 149.8 – 112

(1)

(2) 18(3) 324(4) 24(5) None of these15. (27)

2 × 6 ÷ 9 + (7)

3 + 71 = (?)

3 – 431

(1) 11(2) (13)3 (3) 13(4)

(11)

2

(5) None of theseDirections (Q. 16-20): What will come in


questions? (Corporation Bank PO Exam

2011)

16. 5907 – 1296 ÷ 144 = ? 8

(1) 726.75(2) 767.25(3) 737.25(4) 676.75(5) None of these17.


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(1) (2)

(3) 3(4) 9(5) -318.

(1) 11(2) 5(3) 7(4) 9(5) None of these19.

(1) (2) 200(3) (4) 100(5) –1020.

(1) 169(2) 13(3) 14(4) 196(5) None of these


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26 IBPS PO EXAM 2013 : Quantitative Aptitude

9. (0·81)2+ (0·729)

3x (0·9)

2 = (0.9)

?-3

(1) 6(2) 2(3) 4(4) 0(5) None of these10. 65% of x 5 =? + 154

(1) 56(2) 28(3) 35(4) 32(5) None of theseDirections-(Q. 11-15) What approximate

value will come in place of question-mark

(?) in the

following questions? (Allahabad Bank

Probationary Officers Exam 2011)

(You are not expected to calculate the

exact value.)

11. =? ÷ 8

(1) 620(2) 670(3) 770(4) 750(5) 700

12. 89·988% of 699·9 + 50·002% of 999·99 -

170·015 =?

(1) 990(2) 900(3) 920(4) 960(5) 86013. ÷ =?

(1) 760(2) 800(3)

690(4) 870

(5) 78014. 6999 ÷70·005 x 94·998 =? x 19·999

(1) 475(2) 420(3) 320(4) 540(5) 52515. (49·99)2 – (8·9)2 – (15·9)2 =?

(1) 2165(2) 2000(3) 1965(4) 1920(5) 1885


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Simplification & Approximaiton Averages Practice Set-1

(Answers)

1) 5

2) 1

3) 1

4) 4

5) 3

6) 4

7) 2

8) 2

9) 5

10) 3

11) 2

12) 4

13) 1

14) 5

15) 1

16) 3

17) 2

18) 4

19) 5

20) 2


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Simplification & Approximaiton Averages Practice Set-2

(Answers)

1) 1

2) 1

3) 5

4) 3

5) 5

6) 3

7) 3

8) 5

9) 4

10) 2

11) 2

12) 4

13) 4

14) 1

15) 1


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Chapter: Number Series In Number Series, questions are asked on the basis of relation between numbers given in a

series. The questions asked can be divided into different types:

Type I: In this type of questions, a series of numbers is given with one number missing

represented by a question mark. Candidate has to select from the options choices to correct

option in place of the question mark. The given sequences of numbers will be such that each

number follows its predecessor in the same way, i.e., according to a particular pattern.

Candidates are required to find out the correct ways in which the sequence is formed and there

after find out the number to complete the series.

1. 30, 34, 43, 59, 84, 120,?

(1) 169

(2) 148

(3) 153

(4) 176

(5) None of these

Solution: (1) The given pattern is:

+22, 3

2, +4

2, + 6

2, +7

2

So, missing term is 169=120 +72

2. 40, 54, 82,?, 180,250

(1) 142

(2) 124

(3) 136

(4) 163

(5) None of these

Solution: (2) The pattern is: +14, + 28, + 42, + 52, + 70


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So, missing term is 82 + 42=124

Type II: Here, we are given a sequence of number. Whole sequence, except the odd number

follow a certain rule. You have to find that number which does not follow the rule.

1. 0, 1,3,8,18,35,264

(1) 62

(2) 35

(3) 18

(4) 8

(5) None of these

Solution: (1) The pattern is +(02+1), +(1

2+1), + (2

2+1) ,+ (3

2+1), + (4

2+1), + (5

2+1)

So, 62 is wrong and must be replaced by 35 + (52+1) = 62

2. 1, 9, 125, 49, 729, 121, 2147

(1) 2147

(2) 729

(3) 125

(4) 1

(5) None of these

Solution: (1)

Type III: In this type of questions, a number series is given. After the series is over, in the next

line, a number is followed by (A), (B), (C), (D) and (E). The candidates have to complete the

series starting with the number given following the sequence of the given series.

1. 2, 4, 9, 20, 43, 90

3 (A) (B) (C) (D) (E)

Which number will come in place of (D)?

(1) 58

(2) 99


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(3) 48

(4) 59

(5) None of these

Solution: (4)

Similarly,

Hence, the number 59 will come in place of D.

2. 3, 4, 10, 33, 136,

3 (A) (B) (C) (D) (E)

Which number will come in place of (E)?

(1) 1035

(2) 1165

(3) 1039

(4) 891

(5) None of these

Solution: (2)


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Similarly,

Hence, the number 1165 will come in place of E.


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Solved Examples (Number Series)

Directions: (1-5) In each of these questions a number series is given. In each series only one

number is wrong. Find out the wrong number. (IBPS CWE PO MT 2012)

1. 5531 5506 5425 5304 5135 4910 4621

(1) 5531

(2) 5425

(3) 4621

(4) 5135

(5) 5506

Solution: The number should be 5555 in place of 5531.

-72, -9

2, -11

2, -13

2, -15

2, -17

2...

Ans: (1)

2. 6 7 9 13 26 37 69

(1) 7(2) 26

(3) 69

(4) 37

(5) 9


+1, +2, +4, +8, +16, +32

Ans: (2)

3. 1 3 10 36 152 760 4632

(1) 3

(2) 36

(3) 4632

(4) 760


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(5) 152

Solution: The number should be 770 In place of 760.

×1 +2, ×2 +4, ×3 +6, ×4 + 8, ×5 +10, ×6 + 12, ...Ans: (4)

4. 4 3 9 34 96 219 435

(1) 4

(2) 9

(3) 34

(4) 435

(5) 219

Solution: The series is 02+ 4, 12+2, 32+0, 62-2, 102-4, 152- 6,212 - 8...

Hence, 435 should be replaced with 433

Ans: (1)

5. 157.5 45 15 6 3 2 1

(1) 1

(2) 2

(3) 6

(4) 157.5(5) 45


3.5, 3, 2.5, 2, 1.5, 1, ...

Ans: (1)

Directions (6-10): In the following number series only one number is wrong.

Find out the wrong number.

6. 7 12 40 222 1742 17390 208608

(1) 7

(2) 12

(3) 40


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(4) 1742

(5) 208608

Solution: The pattern of number series is as follows:

7 2 - 2 = 12

12 4 - (2 + 6) = 48 - 8 = 40

40 6 - (8 + 10) = 240 - 18 = 222

222 8 - (18 + 14) = 1776 - 32 = 1744 1742

1744 10 - (32 + 18) = 17440 - 50 = 17390

Ans: (4)

7. 6 91 584 2935 11756 35277 70558

(1) 91

(2) 70558

(3) 584

(4) 2935

(5) 35277


6 7 + 72 = 42 + 49 = 91

91 6 + 62 = 546 + 36 = 582 584

582 5+52 =2910 + 25=2935

2935 4 + 42 = 11740 + 16 = 11756

11756 x 3 + 32 = 35268 + 9 = 35277

Ans: (3)


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8. 9050 5675 3478 2147 1418 1077 950

(1) 3478

(2) 1418

(3) 5675

(4) 2147

(5) 1077


9050 – I53 = 9050 - 3375 = 5675

5675 - 133

= 5675 - 2197 = 3478

3478 - 113 = 3478 - 1331 = 2147

2147 - 93 = 2147 - 729 = 1418

1418 - 73 = 1418 - 343 = 1075 1077

Ans: (5)

9. 1 4 25 256 3125 46656 823543

(1)3125

(2) 823543

(3) 46656

(4) 25

(5) 256


11 = 1;-2

2 = 4; 3

3 = 27 25; 4

4 = 256; 5

5 = 3125; 6

6 = 46656;

77 = 823543

Ans: (4)


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10. 8424 4212 2106 1051 526.5 263.25 131.625

(1) 131.625

(2) 1051

(3) 4212

(4) 8424

(5) 263.25


8424 2 = 4212

4212 2 = 2106

2106 2 = 1053 1051

1053 2 = 526.5

526.5 ÷ 2 = 263.25

263.25 ÷ 2 = 13 1.625

Ans: (2)


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Practice Set (Number Series)

Directions (Q. 1-3): What will come in place

of question mark (?) in the following

number series? (IBPS RRB Grade Officer

Exam 2012)

1. 987 587 331 187 123 (?)

(1) 104

(2) 113

(3) 107

(4) 114

(5) None of these

2. 125 171 263 401 585 (?)

(1) 835

(2) 815

(3) 792

(4) 788

(5) None of these

3. 121 132 167 226 309 (?)

(1) 424

(2) 413

(3) 427

(4) 416

(5) None of these

Directions (Q. 4-5): In the following

number series, only one is wrong. Find out

the wrong number.

4. 454 327 648 524 842 713 1036

(1) 327

(2) 648

(3) 521

(4) 842

(5) 713

5. 72.5 86 113 168 275 491 923

(1) 86

(2)113

(3)168

(4)275

(5)491

Directions (Q. 6-10): What will come in


number series? (RBI Grade’B’ Officer’s

Exam 2011)

6. 17 19 33 (?) 129 227

(1) 64(2) 73(3) 67(4) 72(5) None of these7. 35 256 451 620 763 (?)


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(1) 680(2) 893(3) 633(4) 880(5) None of these8. 18 139 868 917 (?) 1051

(1) 1042(2) 1036(3) 942(4) 996(5) None of these9. 2890 (?) 1162 874 730

658

(1) 1684(2) 1738(3) 1784(4) 1672(5) None of these10. 14 1004 1202 1251.5 1268 (?)

(1) 1267.5(2) 1276.25(3) 1324.5(4) 1367.25(5) None of theseDirections (Q. 11-15): What will come in


number series? (Corporation Bank PO

2011)

11. 8 11 20 47 128 (?)

(1) 483(2) 488(3) 397(4) 371(5) None of these12. 71 78 99 134 183 (?)

(1) 253(2) 239(3) 246(4) 253(5) None of these13. 342 337.5 328.5 315 297 (?)

265.5

274.5

270

260

None of these

14. 161 164 179 242 497 (?)

(1) 1540(2) 1480(3) 1520(4) 1440(5) None of these15. 239 254 284 344 464 (?)

(1) 726(2) 716(3) 724(4) 714(5) None of theseDirections-(Q. 16-20) What will come in

place of question-mark (?) in the following

number series? (Allahabad Bank

Probationary Officers Exam 2011)

16. 958 833 733 658 608, (?)

(1) 577(2) 583(3) 567(4) 573(5) None of these


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17. 11 10 18 51 200, (?)

(1) 885(2) 1025(3) 865(4) 995(5) None of these18. 25 48 94 186 370 (?)

(1) 738(2) 744(3) 746(4) 724(5) None of these

19. 14 24 43 71 108 (?)

(1) 194(2) 154(3) 3) 145(4) 4) 155(5) 5) None of these20. 144 173 140 169 136 (?)

(1) 157(2) 148(3) 164(4) 132(5) None of these


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Number Series Practice Set (Answers)

1) 3

2) 2

3) 4

4) 5

5) 3

6) 3

7) 4

8) 1

9) 2

10) 2

11) 4

12) 3

13) 2

14) 3

15) 5

16) 2

17) 4

18) 1

19) 2

20) 5


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Chapter: Number System

Introduction:

Number is a symbol which represents quantity. There are three types of numbers:

1. Real Numbers: Real numbers are those numbers which can be easily indentify andquantify.

For example: -10, -7.33, -1, 0, 1, 2, 5.77 etc.

2. Imaginary Numbers: Imaginary numbers are those numbers which we can just imaginebut cannot physically perceive.

For example: , etc, is represented by i . Square root of all negative

numbers are imaginary.

3. Complex Number: Combination of Real and Imaginary number is called complexnumbers.

For example: (2+5i) , (1+3i) etc .

Here we will only discuss about the real numbers .

Types of Real Numbers: there are two types of real numbers

1. Rational numbers: - All that numbers which can be expressed in the form of where p& q are integers and q 0 are called rational numbers.

For example: - -1, 2, , 0, 1 , 2.7 etc. , here -1 = =

Again Rational numbers are classified as:

(a) Integers: All rational numbers which do not have decimal or fractional parts are calledintegers.For example: -3, -1, 0 , 1 , 2 etc .

Integers are of two type whole numbers and natural numbers. All the non negative integers are

whole numbers , for example 0 , 1 , 2 , 3 etc and all the whole numbers except 0 are natural

numbers , for example 1, 2 , 3 etc


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(b) Fractions: All rational numbers which are in the form of where p & q are integers andq 0 and p is not a multiple of q are called fractions.

For example: - 1.2, , , 1.7, .3 etc.

Fractions are of three types:

Proper Improper Mixed fractions

A proper fraction is a fraction whose numerator is smaller than denominator, for example

, etc. An improper fraction is a fraction whose numerator is equal to or greater than its

denominator for example , etc. and a mixed fraction is an integer plus a fraction, for

example , etc.

2. Irrational Numbers:- All that numbers which cannot be expressed in the form of arecalled irrational numbers. They have non-terminating and non-recurring decimal parts.

For example: , , etc.

On the basis of origin:

1. Prime Numbers: All the natural numbers greater than 1 which are only divisible by 1and the number itself are called prime numbers.

For example: 2, 3, 5, 7, 11, 13, 17 etc.

2. Composite Numbers: All the natural numbers greater than 1 which are divisible by atleast one more number other than 1 and the number itself are called composite

numbers.

For example: 4, 6, 8, 9, 10, 12 etc.

Note: 1 is neither a prime number nor a composite.

On basis of divisor:

1. Even Numbers: All the natural numbers which are multiple of 2 are called evennumbers.

For example: 2, 4, 6, 8, 10 etc.


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Odd Numbers: All the natural numbers which are not a multiple of 2 are called odd

numbers. They are denoted as 2k 1, where k is a natural number.

For example: 3, 5, 7, 9, 11 etc.

To find whether a number is prime or not.

Step 1: Find the approximate square root of a number .

Step 2: Check if any prime number from 2 to that square root divides that number or not.

Step 3: If none of those prime number divides the number than the number must be prime

number.

Example: Take 631 , the approx square root of 631 is 25 , now from 2 to 25 there are 2 , 3 ,5

, 7 , 11 , 13 , 17 , 19 and 23 prime number . Since none of these divides 631, so 631 must be

a prime number.

Conversion of recurring decimal into fraction.

The form of purely recurring number =

Let x = 0.77777…. 10x = 7.77777……

If x = 0.27272727 …. 100 x = 27.272727 ……

The form of purely recurring number =

Let x= 0.143333333…….. 100x = 14.333333……. 1000x = 143.3333….

= 129


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Quotient and remainder:

Dividend = (Divisor Quotient) + remainder.

For example: If dividend = 15968, Quotient = 89 and remainder = 37 then Divisor is?

Divisor =

=


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Divisibility Rules:

ForNumber Divisibility Rule Example Note

2 If the last digit of a number

is 0,2,4,6,8 , then the

number is divisible by 2

742 is divisible by 2 but 743 is

not.

3 If the sum of all the digits of

a number is divisible by 3 ,

then the number is divisible

by 3

1458 (sum of digits = 18) is

divisible by 3, but 766 (sum of

digits =19) is not divisible by 3.

766 (sum of digits

=19) the remainder

when 19 is divided by

3 i.e. 1 will also bethe remainder when

766 is divided by3

4 If the last two digits of a

number are divisible by 4,

then the number is also

divisible by 4

6732 is divisible by 4 as 32 is

divisible by 4, but 2142 is not

divisible by 4.

Similarly the

remainder when 42 is

divided by 4 i.e 2 will

also be the

remainder when

2142 is divided by 4.

5 If the last digits of a number

are 0 and 5, then the

number is divisible by 5.

1465, 1320 are divisible by 5

as their last digit is 5 and 0

respectively.

6 If the number is divisible by

2 and 3 both, then it is also

divisible by 6.

1452 is divisible by both 2 and

3 so it is divisible by 6 also,

but 3362 is not divisible by 6

as it is not divisible by 3.

If the number is

divisible by 4 and 6

both, then it is not

necessary that it is

divisible by 24 (6 4).

8 If the last three digit of a

number are divisible by 8 or

are 000, then the number is

divisible by 8 .

43102 and 13000 are divisible

by 8 since 102 is divisible by 8

and 13000 have 000 as last

three digits, but 2148 is not as

The remainder when

148 is divided by 8

i.e. 4 will also be the

remainder of 2148


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148 is not divisible by 8 when divided by 8.

9 If the sum of all digits of a

number is divisible by 9 ,

then the number is also

divisible by 9.

25344 (sum of digits = 18) is

divisible by 9 , 764 (sum of

digits =17) is not.

The remainder when

17 is divided by 9 i.e

8 will also be the

remainder when 764

is divided by 9.

11 If the difference between

the sum of the digits in the

even places and the sum of

the digits in the odd places

is either 0 or is divisible by

11 , then the number is also

divisible by 11.

9415956 is divisible by 11 as

the difference of 9+1+9+6 =25

and 4+5+5 = 14 is 11, but

31872 is not as the sum of

even places = 13 and sum of

odd is 8 their difference is

neither 0 nor 11.


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Solved Examples (Number System)

1. When X is subtracted from the numbers 9, 15 and 27, the remainders are in continued

proportion. What is the value of X? (IBPS CWE PO MT 2012)

(1) 8

(2) 6

(3) 4

(4) 5

(5) None of these

Solution: Let be subtracted from the numbers 9, 15 and 27 we get continue proportion.Now, 9 – : 15 – : 27 –

b2 = ac

(15 – )2 = (9 – ) (27 – )

or, 225 – 30 +2 = 243 +

2 – 36

or, 6 = 243 – 225 = 18

X = 3

Hence number become 9 - x = 9-3=6

15 – x = 15 -3 = 12

And 27-x = 27 -3 = 24

6 : 12 : 24 = 1: 2: 4Thus 1: 2: 4 is continued proportion

Ans: (5)

2. Sum of three consecutive numbers is 2262. What is 41% of the highest number? (IBPS CWE

PO MT 2012)

(1) 301.5.1

(2) 303.14

(3) 308.73

(4) 306.35(5) 309.55

Solution: Let the three consecutive number be x, x + 1 and x + 2.

Then, x + x + 1 + x + 2 =2262

or, 3x = 2262 – 3 = 2259

x = = 753


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The Numbers are 753, 754, 755.

The highest number is 755

41% of 755 = 755 = 41 7.55 = 309.55

Ans: (5)

3. Rachita enters a shop to buy ice-creams, cookies and pastries. She has to buy at least 9

units of each. She buys more cookies than ice-creams and more pastries than cookies. She

picks up a total of 32 items. How many cookies does she buy? (IBPS CWE PO MT 2012)

(1) Either 12 or 13

(2) Either 11 or 12

(3) Either 10 or 11

(4) Either 9 or 11

(5) Either 9 or 10

Solution:

Total number of items = 32

Maximum number of ice creams = 9

pastries> cookies> ice cream

So, 13 10 9

12 11 9

Hence number of cookies is either 10 or 11.

Number of pastries is either 13 or 12.

Ans: (3)

4. The fare of a bus is Rs. x for the first five kilometres and Rs. 13/- per kilometre thereafter. If

a passenger pays Rs. 2402/- for a journey of 187 kilometres, what is the value of X? (IBPS CWE

PO MT 2012)

(1) Rs. 29

(2) Rs. 39

(3) Rs. 36

(4) Rs. 31

(5) None of these

Solution: Let the fare of first five kilometres be Rs. x.

Total distance = 187 km

Remaining distance = 187 - 5 = 182 km

Now, x + 182 13 = 2402


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x = 2402 - 2366= Rs.36

Ans: (3)

5. The product of three consecutive even numbers is 4032. The product of the first and thethird number is 252. What is five times the second number?

(1) 80

(2) 100

(3) 60

(4) 70

(5) 90

Solution: Let the three consecutive even numbers be 2x, 2x + 2 and 2x+4.

Then, (2x) (2x + 2) (2x + 4) = 4032 ... (I)

Again, product of first and third number

2x (2x + 4) = 252 ... (II)

Putting the values of the product of first and third number in eqn (I), we have

(2x + 2) 252 = 4032

or, 2x + 2 = = 16

x = 7

Hence, first number = 7 8 = 14

Second number = 7 x 2 + 2 = 16

And third number = 7 x 2 + 4 = 18

Five times of second number = 5 x 16 = 80

Ans: (1)

6. Rubina could get equal number of Rs. 55, Rs. 85 and Rs. 105 tickets for a movie. She spends

Rs. 2,940 for all the tickets. How many of each did she buy?

(1) 12

(2) 14

(3) 16

(4) Cannot be determined

(5) None of these

Solution: Let she buy x tickets.

Then total money spent = 55x + 85x + 105x

or, 245x = 2940

or, x = 12

Ans: (1)


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7. Seema bought 20 pens, 8 packets of wax colours, 6 calculators and 7 pencil boxes. The price

of one pen is Rs. 7, one packet of wax colour is for Rs. 22, one calculator is for Rs. 175 and one

pencil box costs Rs. 14 more than the combined price of one pen and one packet of wax

colours.How much amount did Seema pay to the shopkeeper?

(1) Rs. 1,491

(2) Rs. 1,725

(3) Rs. 1,667

(4) Rs. 1,527

(5) None of these

Solution: Price of one pencil box = 14 + (Price of one pen + Price of one packet of wax colours)=

14+ (7+22) = Rs. 43

Total amount paid by Seema= {(20 × 7) + (8 × 22) + (6 × 175) + (7 × 43)}

= Rs 1667

Ans: (3)

8. In a cricket match, Sachin and Viru scored a century each (more than 100 runs) and Yuvi

and Gauti scored a half century each. Gauti scored 76 runs and Yuvi scored 12 runs less than

Gauti. Viru scored 102 runs. The sum of the scores of all the four players is 442. How many

runs did Sachin score? (Corporation Bank PO 2011)

(1) 200(2) 210(3) 180(4) 160(5) None of theseSolution: Sachin's score = 442 – 76 – (76 – 12) – 102 = 200

Ans: (1)

9. The sum of seven consecutive even numbers of Set A is 378. What is the sum of a different

set of four consecutive numbers whose lowest number is 23 less than the mean of Set A?

(1) 132(2) 146(3) 156(4) 124(5) None of these


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Solution: Mean of Set A

Lowest number of Set B = (54 – 23) = 31

Sum of the four numbers of Set B= 31 + 32 + 33 + 34 = 130

Ans: (5)

10. The sum of six consecutive even numbers of Set-A is 402. What is the sum of another Set-

B of four consecutive numbers whose lowest number is 15 less than double the lowest

number of set- A? (Allahabad Bank Probationary Officers Exam 2011)

(1) 444(2) 442(3)

440

(4) 446(5) None of theseSolution: Third even number = = 67 - 1 = 66

smallest even number = 62

smallest number of set B = 2 x 62 - 15 = 109

required sum = 109 + 110 + 111+ 112 = 442

Ans: (2)


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Practice Set-1 (Number System)

1. A person on tour has Rs 360 for his daily expense. He decides to extend his tour

programme by 4 days which leads to cutting down daily expense by Rs 3 a day. The number

of days of his tour programme is

(1) 15(2) 20(3) 18(4) 162. Two times a two-digit number is 9 times the number obtained by reversing the digits and

sum of the digits is 9. The number is

(1) 72(2) 54(3) 63(4) 813. If 5 students utilize 18 pencils in 9 days, how long at the same rate will 66 pencils last for 15

students?

(1) 10 days(2) 12 days(3) 11 days(4) None of these4. A man has certain number of small boxes to pack into parcels. If he packs 3, 4, 5 or 6 in a

parcel, he is left with one over; if he packs 7 in a parcel, none is left over. What is the number

of boxes he may have to pack?

(1) 106(2) 301(3) 309(4) 4005. Out of a group of swans, 7/2 times the square foot of the number are playing on the shore

of the pond. The two remaining are inside the pond. What is the total number of swans?

(1) 10(2) 14(3) 12


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(4) 166. In a family, each daughter has the same number of brothers as she has sisters and each son

has twice as many sisters as he has brothers. How many sons are there in the family?

(1) 4(2) 3(3) 2(4) 57. A yearly payment to a servant is Rs. 90 plus one turban. The servant leaves the job after 9

months and received 65 and a turban. Then find the price of the turban.

(1) Rs 10(2) Rs 15(3) Rs 7.50(4) Cannot be determined8. Mr. Mukherjee is 5 yr older to his wife and they have one son and one daughter. If the

daughter is 23 yr younger to his mother, what is the difference in the ages of the brother and

the sister?

(1) 7 yr(2) 12 yr(3) 4 yr(4) 2 yr9. The expenses of a hotel consist of two parts. The first one varies with the number of

inmates, while the second one is fixed. When the numbers of inmates are 275 and 350, the

expenses are Rs 1600 and Rs 1900 respectively. The expenses when the number of inmates is

315, are

(1) Rs 1760(2) Rs 1680(3) Rs 1780(4) Rs 166010. If the numerator of a fraction is doubled and the denominator is increased by 3, the newfraction is 3/5 what is the original fraction, if its denominator is more than twice the

numerator by 1?

(1) 3/7(2) 6/13(3) 1/3(4) 5/11


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Practice Set-2 (Number System)

1. The sum and product of two numbers are 5 and 6, respectively. The sum of reciprocals of

their squares is

(1) (2) (3) (4)

2. The sum of the squares of 3 consecutive positive numbers is 365. The sum of the numbers

is

(1) 30(2) 33(3) 36(4) 45

3. The sum of a natural number and its square equals the product of the first three primenumbers. The number is

(1) 2(2) 3(3) 5(4) 6

4. 47 is added to the product of 71 and an unknown number. The new number is divisible by

7, giving the quotient 98. The unknown number is a multiple of

(1) 2(2) 7(3) 5(4) 3


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5. Two natural numbers are in the ratio 3: 5 and their product is 2160. The smaller of the

number is

(1) 36(2) 24(3) 18(4) 12

6. The sum of two numbers is 10. Their product is 20. Find the sum of the reciprocals of the

two numbers.

(1) 1(2) (3) (4)

7. The sum of the digits of a two digit numbers is 10. The number formed by reversing the

digits is 18 less than the original number. Find the original number.

(1) 81(2) 46(3) 64(4) 60

8. The least number to be subtracted from 36798 to get a number which is exactly divisible by

78 is

(1) 18(2) 60(3) 38(4) 68

9. The sum of first sixty number from one to sixty is divisible by

(1) 13(2) 59(3) 60(4) 61


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10. Eight consecutive number are given. If the average of the two numbers that appear in the

middle is 6, then the sum of the eight given numbers is

(1) 36(2) 48(3) 54(4) 64


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Number System Practice Set-1 (Answers)

1 (2)

2 (4)

3 (3)

4 (2)

5 (4)

6 (2)

7 (1)

8 (4)

9 (1)

10 (1)


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Number System Practice Set-2 (Answers)

1 (1)

2 (2)

3 (3)

4 (4)

5 (1)

6 (3)

7 (3)

8 (2)

9 (4)

10 (2)


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Chapter: Ratio, Proportion & Alligation

Introduction:-

Ratio is the relation which one quantity bears to another of the same kind. The ratio of two

quantities a and b is the fraction and we write it as a: b.

In the ratio a: b, we call a as the first term or antecedent and b, the second term or

consequent.

Note: The multiplication or division of each term of a ratio by the same non- zero number does

not affect the ratio.

Compound Ratio: - It is obtained by multiplying together the numerators for new numerator

and denominators for new denominator.

Example 1. If the ratios are 4:3, 15:20, 2:6 and 3:5 find the compound ratio?

Sol 1. Required ratio =

Duplicate ratio of a: b =

Triplicate ratio of a: b = etc.

Example2. If we divide 4185 into two parts such that they are in ratio 7:2, then find the values

of both the parts?

Sol 2. Let the actual variable be 7x and 2x.

Then 7x+2x = 4185

So, the 1st

part = 7

The 2nd

part = 2

Note:


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The ratio of first , second and third quantities is given by

ac : bc : bd

If the ratio between first and second quantity is a:b and third and fourth is c:d.

a: b

c: d

ac : bc : bd

Similarly, the ratio of first, second, third and fourth quantities is given by

ace : bce : bde : bdf

If the ratio between first and second quantity is a: b and third and fourth is c:d .

a : b

c : d

e : f

ace : bce : bde : bdf

Example 3. If Savita has Rs 1880. How much money does Ravina have if the ratio of money withsavita and Rita is 15: 7 and that with Rita and Ravina 16: 7?

Solution3:

Savita : Rita : Ravina

15 : 7

16 : 7

15

240 : 112 : 14

The ratio of money with Savita , Rita and Ravina is 240 : 112 : 14.

We see that 240 x = 1880

Hence 14


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Proportion

Introduction:-

Four quantities are said to be proportional if the two ratios are equal i.e. the A, B, C and

D are proportion. It is denoted by “::” it is written as A : B : C : D where A and D are extremes

and B and C are called means .

Product of the extreme = Product of the means

Direct proportion: - The two given quantities are so related that if one quantity increases (or

decreases) then the other quantity also increases (or decreases).

Example 1. If 5 pens cost Rs 10 then 15 pen cost?

Sol 1. It is seen that if number of pens increases then cost also increases. So,

5 pens: 15 pens:: Rs 10 : required cost

Required cost =

Inverse proportion: - The two given quantities are so related that if one quantity increases (or

decreases) then the other quantity also decreases (or increases).

Example 2.If 10 men can do a work in 20 days then in how many days 20 men can do that work?

Sol 2. Here if men increase then days should decrease, so this is a case of inverse proportion, so

10 men: 20 men :: required days : 20 days

Required days =

Rule of three: It Is the method of finding 4th

term of a proportion if all the other three are given,if ratio is a:b :: c:d then ,

d =

Compound proportion: - Lets take an example to explain this.


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Example3. If 9 men can do a piece of work in 40 days of 10 hours each, how many men will it

take to do 12 times the amount of work if they work for 30 days of 9 hours?

Solution 3:

Step 1. Days: ……. : …….

Hours: ……. : …….. :: 9: required no. of men

Work: ……. : ……..

Step 2.

1. Compare days with men : to do the work in less days we will need more men , so it is thecase of inverse proportion hence ,

30 : 40 :: 9 : required no. of men2. Compare hours with men : to do the work in less hours we will need more men , so it is

the case of inverse proportion hence ,

9 : 10 :: 9 : required no. of men3. Compare work with men : to do the more work we will need more men , so it is the

case of direct proportion hence ,

1: 12:: 9: required no. of men

Put all the values in step 1,

30: 40

9: 10 :: 9: required no. of men

1: 12

Now,


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ALLIGATION

Introduction:-

The word allegation means linking. It is used to find:

1. The proportion in which the ingredients of given price are mixed to produce a newmixture at a given price.

2. The mean or average value of mixture when the price of the two or more ingredientsand the proportion in which they are mixed are given.

Mathematical Formula:

For two ingredient:-

CP of unit quantity of cheaper (c) CP of unit quantity of dearer (d)

Mean Price

(d-m) (m-c)

Then (cheaper quantity): (dearer quantity) = (d-m): (m-c)

Example 1: If the rice at Rs 3.20 per kg and the rice at Rs 3.50 per kg be mixed then what

should be their proportion so that the new mixture be worth Rs 3.35 per kg ?

Sol 1: CP of 1 kg of cheaper rice CP of 1 kg of dearer rice

320 paisa 350 paisa

Mean Price (m)

335 paisa

15 15


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By allegation:

Hence they must be mixed in equal proportion i.e. 1:1

For three ingredient:-

1. The price of the ingredient should be reduced to one denomination and then placethem in ascending order under one another.

2. After that place the mean prices to the left of all the price3. Then pair the price so that price less than and greater than the mean prices go together.4. Then find out the difference between mean price and each price and place it opposite to

the price with which it is linked.

5. These difference will help to find out the given answer and similarly it will work for fouringredients .

Example 2: Find out the ratio of new mixture so that it will cost Rs 1.40 per kg from the

given three kinds of rice costing Rs 1.20, Rs 1.45 and Rs 1.74?

Sol 2: 1st

rice cost = 120, 2nd

rice cost = 145 and 3rd

rice cost = 174 paisa.

From the above rule: we have,

120 5+34 [(145-140) + (174-140)]

140 145 20 (140-120)

174 20 (140-120)

Therefore, three rice must be mixed in 39: 20: 20 ratios to have a new mixture of rice.


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Solved Examples (Ratio, Proportion & Alligation)

1. A certain amount was to be distributed among A, B and C in the ratio 2: 3: 4 respectively,

but was erroneously distributed in the ratio 7: 2: 5 respectively. As a result of this, B got Rs 40

less. What is the amount? (IBPS CWE PO MT 2012)

(1) Rs. 210

(2) Rs. 270

(3) Rs. 230

(4) Rs. 280

(5) None of these

Solution: Let the amount be x.

B's share =

Due to error B's share =

Difference in B's share due to error = 40

- = 40

or, = 40

or, 24x = 40 126

x = = Rs. 210

Ans: (1)

2. Rs.73,689/- are divided between A and B in the ratio 4: 7. What is the difference between

thrice the share of A and twice the share of B? (IBPS CWE PO MT 2012)

(1) Rs. 36,699

(2) Rs. 46,893

(3) Rs. 20,097

(4) Rs. 26,796

(5) Rs. 13,398

Solution: Let A’s share be 4x and B’s share be 7x.

4x +7x = 73689

or, 11x = 73689


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x = = 6699

A’s share = 6699 4 = 26796

B’s share = 6699 7 = 44893

Thrice the share of A = 26796 3 = 80388

Twice the share of B = 46893 2= 93786

Difference = 93786 - 80388 = Rs. 13398

Ans: (5)

3. The ratio of the present age of Manisha and Deepali is 5:X. Manisha is 9 years younger than

Parineeta. Parineeta’s age after 9 years will be 33 years. The difference between Deepali's

and Manisha's age is the same as the present age of Parineeta. What should come in place of

X?

(1) 23

(2) 39

(3) 15


(5) None of these

Solution: Parineeta’s present age = (33 - 9 =) 24 yrs.

Manisha's present age = (24 - 9 =) 15 yrs.

Deepali’s present age = IS + 24 = 39 yrs.

Ratio of the present age of Manisha and Deepali

= 15 : 39 = 5 : 13

X = 13

Ans: (5)

4. The ratio between the three angles of a quadrilateral is 3 : 5 : 9. The value of the fourth

angle of the quadrilateral is 71˚. What is the difference between the largest and the smallest

angles of the quadrilateral? (IBPS RRB Group ‘A’ Officers Exam 2012)

(1) 82˚

(2) 106˚

(3) 102˚

(4) 92˚

(5) None of these


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Solution. Let the quadrilateral angles be 3x, 5x, 9x and 71˚.

Total sum of angles = 3x + 5x + 9x + 71˚ = 360˚

or, 17x = 360 – 71 = 289

∴ x = 17°Hence angles are 51˚, 85˚, 153°, and 71˚.

∴ Difference = 153 – 51 = 102˚.

Ans: (3)

5. The second largest and the smallest angles of a triangle are in the ratio of 6 : 5. The

difference between the second largest angle and the smallest angle 'of the triangle is equal to

9°. What is the difference between the smallest and the largest angles of the triangle? (IBPS

RRB Group ‘A’ Officers Exam 2012)

(1) 36°

(2) 24°

(3) 12°

(4) 18°

(4) None of these

Solution. Let the second largest angle of the triangle be 6x and the smallest angle 5x.

Now, 6x - 5x = 9°

or, x = 9°

Second largest angle = 54°

Smallest angle = 45°

Sum of angles of a triangle = 180°

∴ largest angle = 180 - 99 = 810

∴ Difference = 81 - 45 = 36°.

Ans: 1

6. The ratio between the speed of a bus and train is 15 : 27 respectively. Also, a car covered a

distance of 720 km in 9 hours. The speed of the bus is three- fourth the speed of the car. How

much distance will the train cover in 7 hours? (Allahabad Bank Probationary Officers Exam

2011)

(1) 760 km

(2) 756 km

(3) 740 km


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(5) None of these

Solution: Speed of the car = = = 80hm/hr

Speed of the bus = 60km/hr

Speed of the train = 108km/hr

Distance covered by train in 7 hours = (7 x 108 =) 756 km

Ans: (2)


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Practice Set-1 (Ratio, Proportion & Alligation)

1. A container has 80 L of milk. Fromthis container 8 L of milk was taken

out and replaced by water. The

process was further repeated twice.

The volume of milk in the container

after that is [SSC Quantitative

Aptitude (Arihant)]

a) 58.23 Lb) 85.23 Lc) 58.32 Ld) 85.32 L

2. A can contains a mixture of twoliquids A and B in the ratio 7 : 5.

When 9 L of mixture is drawn off

and the can is filled with B, the

ratio of A and B becomes 7 : 9.

Litres of liquid A contained by the

can initially was

a) 10b) 20c) 21d) 25

3. What number should be added toor subtracted from each term of the

ratio 17 : 24 so that it becomes

equal to 1 : 2?

a) 5 is subtractedb) 10 is addedc) 7 is addedd) 10 is subtracted

4. The ratio of weekly incomes of Aand B is 9 : 7 and the ratio of their

expenditures is 4 : 3. If each saves

Rs. 200 per week, then the sum of

their weekly incomes is

a) Rs. 3200b) Rs. 4200c) Rs. 4800d) Rs. 5600

5. The ratio of alcohol and water in 40L of mixture is 5 : 3.8 L of the

mixture is removed and replaced

with water, Now, the ratio of the

alcohol and water in the resultant

mixture is

a) 1 : 2b) 1 : 1c) 2 : 1d) 1 : 3

6. Rama's expenditure and savings arein the ratio 3 : 2. His income

increases by 10%. His expenditure

also increases by 12%. His saving

increases by

a) 7%b) 10%c) 9%d) 13%

7. Three numbers are in the ratio 3 : 4: 5. The sum of the largest and the

smallest equals the sum of the

second and 52. The smallest

number is

a) 20


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b) 27c) 39d) 52

8. The ratio of the ages of Ram andRahim 10 yr ago was 1 : 3. The ratio

of their ages 5 yr hence will be 2 : 3.

Then, the ratio of their present ages

is

a) 1 : 2b) 3 : 5c) 3 : 4d) 2 : 5

9. The ratio of milk and water inmixtures of four container are 5 : 3,

2 : 1, 3 : 2 and 7 : 4, respectively. In

which container is the quantity of

milk, relative to water, minimum?

a) Firstb) Secondc) Thirdd) Fourth

10. In a mixture of 25 L, the ratio ofacid to water is 4 : 1. Another 3 L of

water is added to the mixture. The

ratio of acid to water in the new

mixture is

a) 5 : 2b) 2 : 5c) 3 : 5d) 5 : 3

11. A shopkeeper buys two varieties oftea, the price of the first being

twice the second. He sells the

mixture at Rs 36 per kilogram and

makes a profit of 20%. If the ratio of

quantities of the first and second

variety in these mixture is 3 : 4,

then what is the cost price of each

variety of tea ? [Mission MBA MAT

(Arihant)]

a) Rs 21, 42b) Rs 15, 30c) Rs 16.5, 33d) Rs 17, 34

12. Two liquids are mixed in the ratio 3: 5 and the mixture is sold at Rs 120

with a profit of 20%. If the first

liquid is costlier than the second by

Rs 2 per litre, find the cost of the

costlier liquid per litre.

a) Rs 92.30b) Rs 74.10c) Rs 101.25d) Rs 99.25

13. A grocer buys two kinds of rice atRs 1.80 and Rs 1.20 per kg

respectively. In what proportion

should these be mixed, so that by

selling the mixture at Rs 1.75 per

kg, 25% may be gained?

a) 2 : 1b) 3 : 2c) 3 : 4d) 1 : 2

14. A jar full of whisky contains 40% ofalcohol. A part of this whisky is

replaced by another containing 19%

alcohol and now the percentage of

alcohol was found to be 26. The

quantity of whisky replaced is

a)


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b) c) d)

15. A container contains 240 L of wine.80 L is taken out of the container

everyday and an equal quantity of

water is put into it. Find the

quantity of the wine that remains in

the container at the end of the

fourth day.a) 39.2 Lb) 32 Lc) 42.5 Ld) 47.40 L

16. A tea trader mixed two varieties oftea, one costing Rs 3.50 per kg and

the other costing Rs 4 per kg and

sells 40 kg of the mixture to a

vendor at Rs 4.50 per kg and makesa profit of 20%. How much of each

variety did the vendor mix?

a) 30 kg, 10 kgb) 20 kg, 20 kgc) 10 kg, 30 kgd) None of these

17. A vessel contains 50 L milk. Themilkman delivers 10 L to the first

house and adds an equal quantityof water. He does exactly the same

at the second and third house.

What is the ratio of milk and water

when he has finished delivering at

the third house?

a) 61 : 64

b) 27 : 37c) 16 : 19d) None of these

18. Prabhu purchased 30 kg of rice atthe rate of Rs 17.50 per kg and

another 30 kg rice at a certain rate.

He mixed the two rice and sold the

entire quantity at the rate of Rs

18.60 per kg and made 20% over all

profit. At what price per kg did he

purchase the lot of another 30 kg

rice?

a) Rs 14.50b) Rs 12.50c) Rs 15.50d) Rs 13.50

19. A person has a chemical of Rs 50per litre. In what ratio should water

be mixed in that chemical so that

after selling the mixture at Rs 40

per litre he may get a profit of 50%.

a) 8 : 7b) 9 : 8c) 10 : 7d) 4 : 3

20. A trader has 50 kg of pulses, part ofwhich he sells at 8% profit and the

rest at 18% profit. He gains 14% on

the whole. What is the quantity

sold at 18% profit?

a) 30 kgb) 35 kgc) 40 kgd) None of these


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21. A container of capacity 120 L isfilled with milk and water. 80% of

milk and 40% of water is taken out

of vessel. It is found that the vessel

is vacated by 65%. What is the ratio

of milk to water?

a) 5 : 3b) 6 : 5c) 3 : 5d) 4 : 3

22. How much water should be addedto 60 L of milk at L for Rs 10 so

as to have a mixture worth Rs

per litre?

a) 16 Lb) 15 Lc) 18 Ld) 20 L


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Practice Set-2 (Ratio, Proportion & Alligation)

1. An employer reduces the numberof employees in the ratio 8 : 5 and

increases their wages in the ratio 7 :

9. As a result, the overall wages bill

is

a) increased in the ratio 56 : 69b) decreased in the ratio 56 : 45c) increased in the ratio 13 : 17d) decreased in the ratio 17 : 13

2. A can contains a mixture of twoliquids A and B in the ratio 7 : 5.

When 9 L of mixture is drawn off

and the can is filled with B, the

ratio of A and B becomes 7 : 9.

Litres of liquid A contained by the

can initially was

e) 10f) 20g) 21h) 25

3. What number should be added toor subtracted from each term of the

ratio 17 : 24 so that it becomes

equal to 1 : 2?

e) 5 is subtractedf) 10 is added

g) 7 is addedh) 10 is subtracted

4. The ratio of weekly incomes of Aand B is 9 : 7 and the ratio of their

expenditures is 4 : 3. If each saves

Rs. 200 per week, then the sum of

their weekly incomes is

e) Rs. 3200f) Rs. 4200g) Rs. 4800h) Rs. 5600

5. Rama's expenditure and savings arein the ratio 3 : 2. His income

increases by 10%. His expenditure

also increases by 12%. His saving

increases by

e) 7%f) 10%g) 9%h)

13%

6. If A : B is 2 : 3, B : C is 6 : 11, then A :B : C is

a) 2 : 3 : 11b) 4 : 6 : 22


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c) 4 : 6 : 11d) 2 : 6 : 11

7. The ratio of the ages of Ram andRahim 10 yr ago was 1 : 3. The ratio

of their ages 5 yr hence will be 2 : 3.

Then, the ratio of their present ages

is

e) 1 : 2f) 3 : 5g) 3 : 4h) 2 : 5

8. If the annual income of A, B and Care in the ratio 1 : 3 : 7 and the total

annual income of A and C is Rs.

800000, then the monthly salary of

B is

a) Rs. 20000b) Rs. 25000c) Rs. 30000d) Rs. 15000

9. Two numbers are such that theratio between them is 4 : 7. If each

is increased by 4 the ratio becomes

3 : 5. The larger number is

a) 36b) 48c) 56

d) 6410. Acid and water are mixed in a

vessel A in the ratio of 5 : 2 and inthe vessel B in the ratio of 8 : 5. In

what proportion should quantities

be taken out from the two vessels,

so as to form a mixture in which the

acid and water will be in the ratio

of 9 : 4?

a) 7 : 2b) 2 : 7c) 7 : 4d) 2 : 3

11. In an alloy, Zinc and Copper are inthe ratio 1 : 2. In the second alloy,

the same elements are in the ratio

2 : 3. If these two alloys be mixed to

form a new alloy in which twoelements are in the ratio 5 : 8, the

ratio of these two alloys in the new

alloy is

a) 3 : 10b) 3 : 7c) 10 : 3d) 7 : 3

12. A boy has a few coins ofdenominations 50 paise, 25 paise

and 10 paise in the ratio 1 : 2 : 3. If

the total amount of the coins is Rs.


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6.50, the number of 10 paise coins

is

a) 5b) 10c) 15d) 20

13. The sum of the ages of a father andhis son is 100 yr now. 5 yr ago their

ages were in the ratio of 2 : 1. The

ratio of the ages of father and son

after 10 yr will be

a) 5 : 3b) 4 : 3c) 10 : 7d) 3 : 5

14. In a school having roll strength 286,the ratio of boys and girls is 8 : 5. If

22 more girls get admitted into the

school, the ratio of boys and girls

becomes

a) 12 : 7b) 10 : 7c) 8 : 7d) 4 : 3

15. A box contains Rs. 1,50 paise and25 paise coins in the ratio 8 : 5 : 3. If

the total amount of money in the

box is Rs. 112.50, the number of 50

paise coins is

a) 80b) 50c) 30d) 42


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Ratio, Proportion & Alligation Practice Set-1 (Answers)

1) c2) c3) d4) a5) b6) a7)

c

8) b9) c10) a11) a

12) c13) d14) c15) d16) b17) a18)

d

19) a20) a21) a22) b


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Ratio, Proportion & Alligation Practice Set-2 (Answers)

1) b2) c3) d4) a5) a6) c7) b8) b

9) c10) a11) a12) c13) a14) d15) b


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Chapter: Averages The term Average refers to the sum of all observations divided by the total number of

observations. Average is used quite regular in our day to day life. For example to calculate the

average marks of the students, Average height of a particular group etc. The term average is

also referred to as ‘Mean’. Basic formula to calculate the average is as follows:

Average = ( )

Example. What is the average of First 10 Prime numbers?

Solution: First 10 Prime number are 2,3,5,7,11,13,17,19,23,29.

Hence, Average = {2+3+5+7+11+13+17+19+23+29} / 10

= 129 / 10

= 12.90

So, Average of First 10 Prime numbers is 12.90.

Example. The total number of sales visits made by a Salesman in the month of June is 90.

What is the Average visit he makes per day?

Solution: Number of days in the month of June are 30

Hence, Average Visit per day = Number of total visits / Number of total days

= 90 / 30

= 3

So, the salesman makes 3 visits per day.


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Solved Examples (Averages)

1. Ramola's monthly income is three times Ravina's monthly income. Ravina's monthly income is

fifteen per cent more than Ruchira's monthly income. Ruchira's monthly income is Rs. 32,000. What is

Ramola's annual income?

(1) Rs. 1,10.4

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