Math Special Exam (Solve)

01) 30% of the respondents dislike daily Prothom - alo as their first newspaper. Those who like "Prothom - alo"

as their first newspaper, 50% of them like "Sports news" as their 1st topic. If this research contains total 200

respondents. How many people like Prothom alo but not Sports news as their 1st topic.

02) A cask initially contains pure alcohol up to the brim. The cask can be emptied by removing exactly 5 liters at

a time. Each time this is done, the cask must be filled back to the brim with water. The capacity of the cask is 15L.

When the cask is emptied and filled back to the brim two times, What is the ratio of alcohol to water in the cask.

Special Test for Sonali Bank

Sub : Mathematics

Marks : 50 Time : 30 Min

Here, Dislike Prothom - alo = 30%

Like Prothom - alo = (100% 30%) = 70%

Like Sports news= 50% of 70% = %100100

70

100

50 = 35%

Like Prothom - alo but not Sports news= 70% 35% = 35%.

Number of people like Prothom alo but not Sports news as their 1st topic = 35% of 200 = 70

Answer : 70

Answered all of the following within given region...

02. Here, Pure Alcohol = 15 L

After 1st installment, Alcohol = 15 5 = 10 L & Water = 5 L.

Alcohol : water = 2 : 1

After 2nd installment, Alcohol = 10 3

2 5 = 10

3

10 =

3

20L & Water = 5

3

1 5 + 5 = 10

3

5 =

3

25L

Alcohol : Water = 3

20:3

25 = 20 : 25 = 4 : 5

Answer: 4 : 5

Math Special Exam (Solve)

03) A manufacturer packages soap powder in containers of three different sizes -large, medium and small. The

amount of soap powder in a full large container could fill exactly 3 of the medium containers or exactly 5 of the

small containers. If equal number of small and large containers are to be filled with the amount of soap powder

that would fill 90% medium containers, how many small containers will be filled?

04) Mr. Tanin is planning on depositing a certain amount of money each month into a school fund for his

children. He then decided not to make any contributions during April and May. To make the same annual

contribution that he had originally planned, by what percent should he increase his monthly deposits ?

05) Solve the equation, 2x+1 + 2x-1 = 320

03. Let, Large containers needed x units So, Small containers needed 5x units

According to problem, x + 5x = 90 6x = 90 x = 15

Small containers needed = 5 15 = 75

Answer : 75

04. Let, Mr. Tanin deposited tk x per month So, After 12 month his deposit will be = 12x

If, he did not pay in April, May and June. The deposit will be = 12x 3x = 9x

If he makes same amount, then, He have to increase = x

x

9

3 100% = 30% amount.

Answer : 30%

05) Given that, 2x+1 + 2x-1 = 320

=> 2x.2 +2

2 x = 320 => 2x (2 +

2

1) = 320

=> 2x = 128 => 2x = 27

x = 7

Required Solution, x = 7

Math Special Exam (Solve)

06) In a class of all of the 70 Students takes either Physics, Chemistry or Math. Among them 40 Students opt

Physics, 35 opt Chemistry and 30 opt Math. 15 students opt all of them. How Many students opt. only two (2)

courses?

Here, Total Respondent, (S) = 70

Physics, n(A) = 40 Chemistry, n(B) = 35

Math, n(C) = 30 All, n( ABC) = 15

Taking two Courses , n( AB) + n( BA) + n(C A) = x

According to problem, n(ABC) = n(A) + n(B) + n(C) n( AB) n(BC) n(CA) + n( ABC)

15x30354070 x = 50

Taking only two Courses, = x 3 n( ABC) = 50 3 15 = 5

Answer : 5

07) A person started his journey at 8 am in 3kph and reached his office 45 min late. Next day he started his

journey at 5kph and reached 15 min earlier. Find the distance between home and office.

08) Two cars were starting a race from same point and same direction with 25 ms-1 & 30 ms-1 in a circular

racetrack. If the diameter of the racetrack is 140 m. Find the required time when two cars will meet.

07) Let, Distance = D

Here, Speed, S1 = 3 kph & S2 = 5kph

According to problem, 3

D- 5

D= 1 => 1

15

2

D D = 7.5 Km

Answer : 7.5 Km

08) We know that, When a car round a Circular field across the distance equal to perimeter.

Distance = Perimeter, D = 2r = 2 7

22 70 = 440 m = 0.44 km

Though the car moves on the same direction, So speed, S = 30 25 = 5 kph

Required time to meet = Time

ceDis tan =

5

44.0 = 0.0628 Hr = 0.0628 3600 sec = 226.28 sec

Answer : 226.28 Sec

A B

C

Math Special Exam (Solve)

09) If 5 added to the sum of two digits of a number consisting of two digits, the sum will be 3 times of the digit

tens place. Moreover, If the places of the digit are interchanged, the number thus found will be 9 less than the

original number. Find the number.

10) A bus is travelling with 52 passengers, When it arrives at a stop, y passengers get off and 4 get on. At the

next stop 1/3 of the passengers get off and 3 get on. There are now 25 passengers. Find out how many

passengers get off at the 1st Stop.

09) Let, Unit digit = x & Decimal Digit = y So, The Number = x + 10y

At 1st condition, x + y + 5 = 3y => 2y x = 5 (i)

At 2nd Condition, x + 10y (10x + y) = 9 => 9y 9x = 9 y x = 1 . (ii)

Solving equation (i) & (ii), x = 3 & y = 4

The number = 3 + 10.4 = 43

Answer : 43

10) Here, Total Passenger at the beginning of the trip is = 52

At First Stoppage, Passenger remain = 52 y + 4 = 56 y

At Second Stoppage, If 1/3rd Passenger get off then 2/3rd passengers must remain.

According to problem, 3

2(56 - y) + 3 = 25 =>

3

2(56 - y) = 22 => 56 y = 33 y = 23

Answer : 23