Important Questions On Pipes and Cisterns

1. Two pipes can fill a cistern in 20 and 30 minutes each respectively. When both the pipes were opened together to fill the cistern, it took 3 minutes longer than usual to fill up the cistern because of a leakage through a hole in the bottom of the cistern. If the cistern is full, in how many minutes, it will get emptied because of the leakage?

A. 10 minutes
B. 20 minutes
C. 30 minutes
D. 60 minutes

Solution: If the two pipes are opened together, then the part filled in one minute = + = = = part
So it will take 12 minutes to completely fill the tank.
Time taken to fill the tank due to the hole
= 12 + 3 = 15 min.
Hence empty part in 15 min. =( )* 3 = =

Time taken to empty the entire tank = 15 x 4 = 60 min.

2. A cistern has two pipes. One can fill it in 8h and other can empty it in 5 h. In how many hours will the cistern be emptied if both the pipes are opened together when ¾ of the cistern is already full of water?

B. 10 h
C. 6 h
D.

Solution:

Part of cistern emptied in 1 h
=
∴ part is emptied in 1 h
∴ part is emptied in

3. A cistern can be filled by two supply pipes in 20 minutes and 30 minutes respectively. but a waste pipe can empty it in an hour. Both the supply pipes were opened together to fill the empty cistern, but by mistake, the waste pipe was also open. How much later was the waste pipe closed, if the cistern is filled in 14 minutes?

A. 6 minutes
B. 8 minutes
C. 10 minutes
D. 12 minutes

Solution:

Let the waste pipe be closed after x minutes.

4. Two pipes A and B can fill a cistern in minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:

A. 5 min
B. 9 min
C. 10 min
D. 15 min

Solution:

Let B be turned off after x minutes. Then,
Part filled by (A + B) in x min + Part filled by A in (30 -x) min = 1

5. Two pipes can fill a cistern in 8 and 12 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom of the cistern, it takes 72 minutes extra for the cistern to be filled up. When the cistern is full, in what time the leak empty it?

A. 12 hours
B. 48 hours
C. 24 hours
D. 6 hours

Solution:

Part of tank filled in one hour when there is no leakage in the tank
=1/8+1/12
=5/24
So, tank should be filled by A and B together,
=24/5 * 60=288 min.
Due to leakage total time to fill tank,
=288+72=360 min= 6 hours
1 hour work for leak
=1/8 + 1/12 – 1/6
=6+4 – 8/48
=24 hours.

6. A cistern can be filled by two pipes A and B in 20 and 30 minutes respectively. Both the pipes are opened together when the cistern is empty, but after some time A is stopped and the cistern is filled in 18 minutes is all. The time (in min) after which A is stopped, is

A. 9
B. 12
C. 6
D. 8

Solution:

7. Two pipes, P and Q can fill a cistern in 15 and 18 minutes respectively. If both are opened together and at the end of 3 minutes, Q is closed, how much longer will the cistern take to fill?

A. 8.75 minutes
B. 9.50 minutes
C. 10.25 minutes
D. 10.50 minutes

Solution:

Let the total time taken by the pipes be t.
Pipe P fills the cistern in 15 minutes
So, in 1 minute, Pipe P will fill = 1/15 part of cistern
In 3 minutes, pipe P will fill (1/15) × 3 = 1/5 part of cistern
Similarly, Pipe Q will fill 3/18 = 1/6 part of cistern.
So collectively in the first three minutes both the pipes will fill 1/5 + 1/6 = 11/30 part of the cistern and then Q was closed.
The remaining part 1− 11/30 =19/30 part of the cistern is needed to be filled by P.
Since the time taken by P to fill 1 cistern = 15 minutes
Time taken by P to fill 19/30 of the cistern = 15 ×19/30 = 9.5 minutes
So, P takes 9.5 more minutes to fill the cistern.

8. Two pipes can fill a cistern in 12 min and 15 min respectively. A third pipe can empty the cistern in 20 min. How long will it take to fill the cistern if all the three pipes are opened at the same time?

A. 6 min
B. 8 min
C. 10 min
D. 12 min

Solution:

Time taken to fill the cistern all the three pipes are opened

[Here ]
Required time

9. A cistern has 3 pipes A, B and C. A and B can fill it in 3h and 4 h respectively while C can empty the completely filled cistern in 1 h. If the pipes are opened in order at 3, 4 and 5 pm respectively. At What time will the cistern be empty?

A. 6:15 pm
B. 7:12 pm
C. 8:23 pm
D. 8:35 pm

Solution:

Pipe A is opened at 3 pm, pipe B at 4 pm and the pipe C at 5 pm
Part of the tank filled by pipe A in
Part of the tank filled by pipe B in
Part of the tank filled till 5 pm
Remaining part
Net part emptied when A, B and C are opened
  Part is emptied in 1 h
  is emptied in  2h 12 min
Hence, the tank will be emptied at 7:12 pm.