Bank Math Master

Question: Two pipes A and B can fill a tank in 25 and 50 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?

Solution:
pipe A fill a tank in 25 minutes
so, it fills in one minute (1/25) part

pipe B fill a tank in 50 minutes
so, it fills in one minute (1/50) part

both pipes fill in one minute = (1/25) + (1/50) part
= 3/50 part

So, it will take to fullfill the tank = 1/(3/50) minutes
= 50/3 minutes

Question: While working 9 hour a day, A alone can complete a piece of work in 5 days and B alone in 10 days. In what time would they complete it together, 6 hour a day?

Solution:
A can complete the work in 9 × 5 = 45 hours
1 hour's work of A = 1/45 part

B can complete the work in 9 × 10 = 90 hours
1 hour's work of B = 1/90 part

(A + B)'s 1 hour's work = (1/45) + (1/90) part
= (2 + 1)/90 part
= 3/90 part
= 1/30

∴ Time taken by (A + B) working 6 hours daily = 30/(1 × 6)
= 5 days

Question: 2/5 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 us consider,
The tank has 5x liters of total capacity and holds 2x litres of water.
And if 30 liters of water is taken out, then the tank becomes empty.

It means 2x litres of water is taken out.
∴ 2x = 30 liters
⇒ x = 15 liters

Capacity of tank = 5x
= 5 × 15
= 75 liters

Question: Neha completes 75% of a work in 15 days. Then she calls in Farin, and together they finish the remaining work in 4 days. How long would Farin alone take to complete the whole work?

Solution:
Here,
Neha does 75% or 3/4 work in 15 days
in one day, she does = (3/4 ÷ 15) = 1/20 part
in 4 days, she does 4/20 = 1/5 part

work remaining = 1/4 - 1/5
= 1/20 part

Farin does 1/20 parts in 4 days
she will complete the work {4 ÷ (1/20)} days
= 80 days

Question: Fifteen women can do a work in sixteen days. Twelve men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?

Solution:
Given,
15 women can do a work in 16 days
(15 × 16) = 240 women can complete the work in 1 day
∴ 1 woman's 1 day's work = 1/240

12 men can complete the work in 15 days
(12 × 15) = 180 men can complete the work in 1 day.
∴ 1 man's 1 day's work = 1/180

So, required ratio = 1/180 : 1/240
= 240 : 180
= 4 : 3

Question: If 10 men or 15 boys can make 260 mats in 20 days, then how many mats will be made by 8 men and 12 boys in 20 days?

Solution:
Here
10 men = 15 boys
∴ 1 men = 15/10 boys 
∴ 8 men = (15 × 8)/10 boys
= 12 boys

∴ 8 men and 12 boys = (12 + 12) = 24 boys

15 boys can make in 20 days 260 mats 
∴ 1 boys can make in 20 days 260/15 mats 
∴ 24 boys can make 260 mats in (260 × 24)/15 mats 
= 416 mats 

Question: A and B together can do a piece of work in 20 days. A and B having worked for 10 days, B finishes the remaining work alone in 24 days. In how many days shall B finish the whole work alone?

Solution:
A and B together in 20 days can do a piece of work
A and B together in 1 days can do 1/20 part
A and B together in 10 days can do (1 × 10)/20 part
= 1/2 part

So remaining work = (1 - 1/2) part
= 1/2 part

ATQ,
B finishes 1/2 part in 24 days.
∴ B finishes 1 part in (24 × 2) days
= 48 days

Question: Two pipes A and B can fill a tank in 8 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank?

Solution:
Given,
Pipe A can fill the tank in 8 minutes,
so its rate is 1/8 of the tank per minute.

Pipe B can fill the tank in 20 minutes,
so its rate is 1/20 of the tank per minute.

∴ Part filled in 1 minutes = (1/8 + 1/20)
Part filled in 4 minutes = (1/8 + 1/20) × 4
= 7/10

∴ Remaining part = (1 - 7/10) = 3/10

1/20 Part filled by B in 1 minute
∴ Full Part filled by B in 20 minutes
∴ 3/10 Part filled by B in (20 × 3)/10 minutes
= 6 minutes

The tank will be full in (4 + 6) minutes
=10 minutes