Pipe & cistern
Concept
Pipe and Cistern is basically time & work related math. This method presents the problems like how much time is required to empty or fill the reservoir and capacity of the reservoir. Be sure to understand the terminologies like inlet & outlet clearly.
Inlet: A pipe which is connected to fill a tank is known as inlet.
Outlet: A pipe which is connected to empty a tank is known as outlet.
Tips to solve problem on Pipe & Cistern:
- If a pipe can fill a tank in x hours, in 1 hour it can fill 1/x portion of the tank.
If a pipe can empty a tank in y hours, in 1 hour it can empty 1/y portion of the tank.
- If both are open, in 1 hour {(1/x) – (1/y)} portion of the tank is filled.
- If two pipes A and B alone can fill the tank in x hours and y hours respectively, both in 1 hour can fill {(1/x) + (1/y)} portion of the tank.
Q. A tank can be filled by two pipes A and B in 12 hours and 15 hours respectively. If both the pipes are opened together, how long will it take to fill the tank?
A) 6 hours
B) 7 hours
C) 8 hours
The part of the tank filled by pipe A in one hour is 
and by pipe B in one hour is 
. So, the part of the tank filled by both the pipes in one hour is 
= 
= 
. Therefore, the time taken to fill the tank by both the pipes is 
= 
hours, which is approximately 
hours.
and by pipe B in one hour is . So, the part of the tank filled by both the pipes in one hour is = = . Therefore, the time taken to fill the tank by both the pipes is = hours, which is approximately hours.
D) 9 hours
Discuss
Q. A cistern has two taps that can fill it in 10 minutes and 15 minutes respectively. There is also a waste pipe that can empty the full cistern in 12 minutes. If all the three pipes are opened together, how long will it take to fill the cistern?
A) 12 minutes
The part of the cistern filled by the first tap in one minute is 
and by the second tap in one minute is . The part of the cistern emptied by the waste pipe in one minute is . So, the net part of the cistern filled in one minute is 
= 
= . Therefore, the time taken to fill the cistern by all the three pipes is 
= 12 minutes.
and by the second tap in one minute is . The part of the cistern emptied by the waste pipe in one minute is . So, the net part of the cistern filled in one minute is = = . Therefore, the time taken to fill the cistern by all the three pipes is = 12 minutes.
B) 10 minutes
C) 12 minutes
D) 14 minutes
Discuss
Q. A pipe can fill a tank in 20 minutes and another pipe can fill it in 30 minutes. Both the pipes are opened for some time and then the first pipe is closed. If the tank is filled in a total of 18 minutes, for how long was the first pipe opened?
A) 15 minutes
B) 13 minutes
C) 11 minutes
D) 9 minutes
Let x be the time for which the first pipe was opened. Then, the part of the tank filled by the first pipe in x minutes is 
and by the second pipe in (18-x) minutes is 
. Since the tank is full, we have 
. Solving for x, we get 
.
and by the second pipe in (18-x) minutes is . Since the tank is full, we have . Solving for x, we get .
Discuss
Q. Two pipes A and B can fill a tank in 24 minutes and 32 minutes respectively. If both the pipes are opened simultaneously, after how much time should B be closed so that the tank is full in another 18 minutes?
A) 6 minutes
B) 8 minutes
C) 10 minutes
D) 12 minutes
Let x be the time for which both the pipes are opened together. Then, the part of the tank filled by pipe A in x minutes is 
and by pipe B in x minutes is 
. The remaining part of the tank to be filled in another 18 minutes is 
. Since we want to close pipe B after x minutes, we have 
. Solving for x, we get 
.
and by pipe B in x minutes is . The remaining part of the tank to be filled in another 18 minutes is . Since we want to close pipe B after x minutes, we have . Solving for x, we get .
Discuss
Q. A leaky cistern can be emptied by a drain pipe in eight hours. When there is no leakage, it can be filled by a supply pipe in six hours. How long will it take to fill up when both pipes are open?
A) Cannot be determined
B) Cannot be filled at all
C) Can be filled in less than six hours
D) Can be filled in more than six hours
The rate of filling by the supply pipe is 
per hour and the rate of emptying by the drain pipe is 
per hour. The net rate of filling when both pipes are open is 
per hour, which is positive. Therefore, the cistern can be filled, but at a slower rate than when only the supply pipe is open. Hence, it will take more than six hours to fill up.
per hour and the rate of emptying by the drain pipe is per hour. The net rate of filling when both pipes are open is per hour, which is positive. Therefore, the cistern can be filled, but at a slower rate than when only the supply pipe is open. Hence, it will take more than six hours to fill up.
Discuss
Q. A tank has three pipes A, B and C. Pipe A can fill the tank in 12 hours, pipe B can fill it in 15 hours and pipe C can empty it in 10 hours. If all the pipes are opened together when the tank is empty, how long will it take to fill the tank?
A) 20 hours
The part of the tank filled by pipe A in one hour is , by pipe B in one hour is and by pipe C in one hour is 
. So, the net part of the tank filled in one hour is 
= 
= 
. Therefore, the time taken to fill the tank by all the pipes is 
= 
hours.
, by pipe B in one hour is and by pipe C in one hour is . So, the net part of the tank filled in one hour is = = . Therefore, the time taken to fill the tank by all the pipes is = hours.
B) 30 hours
C) 40 hours
D) 60 hours
Discuss
Q. A cistern has a capacity of 120 litres. It has two inlet pipes that can fill it with water at the rates of 4 litres per minute and 5 litres per minute respectively. There is also an outlet pipe that can drain water from the cistern at the rate of 3 litres per minute. If all the three pipes are opened at the same time when the cistern is empty, how much water will be in the cistern after 12 minutes?
A) 48 litres
B) 60 litres
C) 72 litres
The net rate of filling the cistern by all the three pipes is (4 + 5 - 3) litres per minute, which is 6 litres per minute. So, the amount of water filled in the cistern after 12 minutes is (6 x 12) litres, which is 72 litres.
D) 80 litres
Discuss
Q. A pipe can fill a tank with water in five hours. Due to a leak at the bottom of the tank, it takes six hours to fill the tank. If the tank is full, how long will it take for the leak to empty it?
A) 15 hours
B) 20 hours
C) 25 hours
D) 30 hours
Let x be the rate of filling by the pipe and y be the rate of emptying by the leak. Then, we have 
and 
. Solving for y, we get 
. Therefore, the time taken for the leak to empty the tank is 
, which is 30 hours.
and . Solving for y, we get . Therefore, the time taken for the leak to empty the tank is , which is 30 hours.
Discuss
Q. A cistern has two taps P and Q that can fill it with hot and cold water respectively. Tap P can fill the cistern with hot water in four hours and tap Q can fill it with cold water in six hours. If both taps are opened together when the cistern is empty, what will be the temperature of water in the cistern when it is full? Assume that hot water has a temperature of 80°C and cold water has a temperature of 20°C and that there is no heat loss during the process.
A) 40 C
B) 50 C
Description not available. Let’s discuss.
C) 60 C
D) 70 C
Discuss
