Bank Math Master

Question: A group of men decided to do a job in 5 days. But since 10 men dropped out every day, the job completed at the end of the 7th day. How many men were there at the beginning?

Solution: 
Let X be the initial number of men then,
According to the question,
5X = X + (X - 10) + (X - 20) + (X - 30) + (X - 40) + (X - 50) + (X - 60)
or, 5X = 7X - 210
or, 2X = 210
or, X = 210/2
or, X = 105

Question: Two pipes A and B can fill a tank in 20 and 30 hours respectively. If both the pipes are used together, then how long will it take to fill the tank?

Solution: 
Part filled by A in 1 hour = 1/20

Part filled by B in 1 hour = 1/30

Part filled by (A + B) in 1 hour
= 1/20 + 1/30 = 5/60 = 1/12

∴ Both pipes can fill the tank in 12 hours

Question: While working 7 hour a day, A alone can complete a piece of work in 6 days and B alone in 8 days. In what time would they complete it together, 8 hour a day?

Solution: 
A can complete the work in 7 × 6 = 42 hours
1 hour's work of A = 1/42

B can complete the work in 7 × 8 = 56 hours
1 hour's work of B = 1/56

(A + B)'s 1 hour's work
=1/42+1/56=4+3/168=7/168

∴ Time taken by (A + B) working 8 hours daily
168/7 = 24 hour

∴ as  the will work 8 hour a day, it will take = 24/8 = 3 days

Question:  A man and a boy received 6000 Tk. as wages for 5 days for the work they did together. The man's efficiency in the work was double that of the boy. What are the daily wages of the boy?

Solution: 
Ratio of 1 day's work of man and boy = 2 : 1
Total wages of the boy = (6000 × 1/3)
= 2000 Tk.

∴ Daily wages of the boy= 2000/5 = 400Tk.

Question: A pipe can fill a cistern in 6 hour. After adding another pipe the whole process took only 4 hour. The second pipe alone can do it in- 

Solution: 
Let the socond pipe can do the work in X hours
so in one hour it can fill = 1/X of the cistern

the first pipe can do in one hour = 1/6 of the cistern

ATQ,
1/X + 1/6 = 1/4
(6 + X)/6X = 1/4
6X = 24 + 4X
x = 12
∴ the second pipe can fill the cistern in 12 hours.

Question: 3/7 part of the tank is full of water. When 30 liters of water is taken out, the tank becomes empty. The capacity of the tank is -

Solution: 
Let the capasity of the tank is = X litres

Atq,
3X/7 = 30
X = 70 litres

Question: A man, a woman and a boy can do a piece of work in 6, 9 and 18 days respectively. How many boys must assist one man and one woman to do the work in 1 day ?

Solution: 
(1 man + 1 woman)'s 1 day's work
= 1/6 + 1/9
= 5/18
Remaining work=(1 − 5/18)
=13/18

Work done by 1 boy in 1 day = 1/18

∴Number of boys required= (13×18)/18 boys
=13 boys

Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 7/3 hours to fill the tank. The leak can drain all the water of the tank in:

Solution:
Let, the leak can drain the full water in X hours
in one hour,
the leak drains 1/X
the pump pores 1/2

so, in one hour the tank fills = 1/2 - 1/X
= (X - 2)/2X

Atq,
2x/(X - 2) = 7/3
6X = 7X - 14
X = 14

So, the leak will drain the whole water in just 14 hours.

Question: A tank is filled in 8 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

Solution: 
Let,
C can fill the tank in X hours
∴ B can do it in 2X hours and,
A can do it in 4X hours.

in one hour all the pipes can fill = (1/X + 1/2X + 1/4X)
= 7/4X

ATQ.
4X/7 = 8
X = 56/4
= 14 
∴ time required for A is = 4 × 14 = 56 hours

Question: Rakib can do a certain work in 14 days. After half the work is done Rakib got sick and skip the work for 5 days. After he returns, he started doing the rest of the work in half of his previous efficiency. Total time to finish the work is- 

Solution: 
half of the work is done in 7 days and the rate of work per day is 1/14
afte the effiency became half, work per day = 1/28
∴ half of the work will take = 28/2 = 14 days

∴ total time to do the work is = 7 + 5 + 14 days
= 26 days

Question: 2 leak A and B can drain a cistern in 10 and 20 hours individually. If both the leaks work together, the time required to drain haft of the cistern's water is-

Solution: 
in one hour 2 leaks can drain = 1/10 + 1/20
= 3/20 of the cistern

so, time to drain the whole cistern is = 20/3 hours
∴ half of the cistern in = 20/6 = 10/3 hours

Question:  5 men or 10 women can do a task in 20 days both. If 5 men and 5 women is assigned for the task, how much time will it take to complete it?

Solution: 
5 men can do in one day = 1/20

10 women can do in one day = 1/20
∴ 5 women can do in one day = 1/40

so in one day 5 men and 5 women can do = 1/20 + 1/40
= 3/40

∴ time required to do the full task = 40/3 days

Question: Half of a cistern is filled by pipe A in 4 hours whereas drained by pipe B in 5 hours. How much time will it take to fill the cistern if both the pipes are opened?

Solution:
A can fill the cistern in 8 hours
B can drain it in 10 hours

together they can fill = 1/8 - 1/10 
= 1/40

∴ total time to fill the cistern is 40 hours.

Question: 50 workers can build 50 engines working 8 hours a day. How many workers need to be appointed extra to boost the production to double if they work 10 hours a days?

Solution:
8 hours to build 50 engines by 50 workers
1 hour to build 1 engine by = (50 × 8)/50 workers
10 hours to build 100 engine by = (8 × 100)/10 workers 
= 80 workers

∴ extra workers = 80 - 50 = 30

Question: Pipe A can fill a cistern in 6 hours and B in 4 hours. After filling the half cistern by A, B starting pouring water. Total time to fill the cistern is- 

Solution: 
half of the cistern filled by A in 3 hours.
After that,
bothe the pipes are open.
so in one hour they will pour = 1/6 + 1/4
= 5/12 hours
∴ half of the cisterns will be filled in = 12/(5 × 2) hours
= 12/10 = 1.2 hours

∴ total time = 3 + 1.2 hours
= 4.2 hours