# Pipe and Cistern (5 Questions) -01

Question 01

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

Given:
Pipe A can fill the whole tank in 20 mins
So, Part of the tank filled by Pipe A in 1 minute = 1/20

Pipe B can fill the whole tank in 30 mins
So, Part of the tank filled by Pipe B in 1 minute = 1/30

If both pipes are used together, part of the tank filled in 1 minute = 1/20 + 1/30 = = 5/60 = 1/12

So, 12 minutes are required to fill the tank

Question 02

A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?

Let there are two taps A and B

Tap A can fill the tank in 4 hours
Part of the tank filled by first tap in 1 hour = ¼

Similarly,
Part of the tank emptied by second tap in 1 hour = 1/9

When both taps are opened simultaneously, part of the cistern filled in 1 hour = ¼ – 1/9 = = 5/36
So, the total time taken = 36/5 = 7.2 hours

Question 03

Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in?

Sol:
Pipe A can fill the tank in 5 hours
Part of the tank filled by Pipe A in 1 hour = 1/5

Pipe B fill the tank in 6 hours
Part of the tank filled by Pipe B in 1 hour = 1/6

Pipe C empty the tank in 12 hours
Part of the tank emptied by Pipe C in 1 hour = 1/12

If all three pipes are opened together, part of the filled in 1 hour = 1/5 + 1/6 – 1/12 = 17/60 hours
So, the tank will be filled in = 60/17 hours

Question 04

Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution R in the liquid in the tank after 3 minutes?

Pipe A can fill the tank in 30 minutes
Part of the tank filled by Pipe A in 1 minute =1/30

Pipe B can fill the tank in 20 minutes
Part of the tank filled by Pipe B in 1 minute =1/20

Pipe C can fill the tank in 10 minutes
Part of the tank filled by Pipe C in 1 minute =1/10

Part filled by (A + B + C) in 3 minutes = 3 ( 1/30 + 1/20 + 1/10) = 3 × 11/60 = 11/20
Thus, Part filled by C in 3 minutes = 3/10

Therefore, Required ratio = 3/10 × 20/11 = 6/11

Question 05

Two pipes A and B can separately fill a cistern in 60 minutes and 75 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 minutes. In how much time, the third pipe alone can empty the cistern?

Sol:
Pipe A can fill the tank in 60 minutes
Part of the tank filled by Pipe A in 1 minute =1/60

Pipe B can fill the tank in 75 minutes
Part of the tank filled by Pipe A in 1 minute =1/75

Let the third pipe alone can empty the cistern in x minutes.

As per question- 1/60 + 1/75 – 1/x = 1/50

1/x = 1/60 + 1/75 – 1/50 1/x = 3/300

1/x = 1/100

x = 100 minutes
Thus, the third pipe alone can empty the cistern in 100 minutes