Solution of Written Model TEST for SONALI Bank _ by Arup Dus(1)

Special Test for Sonali Bank Sub : Mathematics Marks : 50

Time : 30 Min

Answered all of the following within given region... 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 1 st topic. If this research contains total 200 respondents. How many people like Prothom – alo but not Sports news as their 1st topic. Here,

Dislike Prothom - alo = 30%  Like Prothom - alo = (100%  30%) = 70%  Like Sports news= 50% of 70% =

50 70   100% = 35% 100 100

 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 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. 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 –

2 10 20  5 = 10 – = L 3 3 3

 Alcohol : Water =

20 25 : = 20 : 25 = 4 : 5 3 3

Answer: 4 : 5 Math Special Exam (Solve)

& Water = 5 –

1 5 25  5 + 5 = 10 – = L 3 3 3

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? 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) 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 ? 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

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

3x  100% = 30% amount. 9x

Answer : 30%

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

2x => 2 .2 + = 320 2 x

=> 2x = 128

=> 2x (2 +

1 ) = 320 2

=> 2x = 27

x=7

Required Solution, x = 7 Math Special Exam (Solve)

= 9x

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

B

A C

All, n( ABC) = 15

Taking two Courses , n( AB) + n( BA) + n(C A) = x

 According to problem, n(ABC) = n(A) + n(B) + n(C) – n( AB) – n(BC) – n(CA) + n( ABC)  70  40  35  30  x  15

 x = 50

 Taking only two Courses, = x – 3  n( ABC) = 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. 07) Let, Distance = D Here,

Speed,

S1 = 3 kph

 According to problem,

&

S2 = 5kph

D D =1 3 5

=>

2D 1 15

 D = 7.5 Km

Answer : 7.5 Km 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. 08) We know that, When a car round a Circular field across the distance equal to perimeter.

 Distance = Perimeter, D = 2πr = 2 

22  70 = 440 m = 0.44 km 7

 Though the car moves on the same direction, So speed, S = 30 – 25 = 5 kph  Required time to meet =

Dis tan ce 0.44 = = 0.0628 Hr = 0.0628  3600 sec = 226.28 sec Time 5

Answer : 226.28 Sec 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. 09) Let, Unit digit = x

&

Decimal Digit = y

At 1st condition,

x + y + 5 = 3y

At 2nd Condition,

x + 10y – (10x + y) = 9

Solving equation (i) & (ii),

So, The Number = x + 10y

=> 2y – x = 5 ……………… (i)

x=3

=> 9y – 9x = 9 &

 y – x = 1 ………………. (ii)

y=4

 The number = 3 + 10.4 = 43

Answer : 43

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. 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,

2 (56 - y) + 3 = 25 3

=>

2 (56 - y) = 22 3

Answer : 23

Math Special Exam (Solve)

=> 56 – y = 33

 y = 23