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Aptitude Pipes and Cisterns Concepts and Formulas

General Terms

A pipe is connected to a tank or cistern. It is used to fill or empty the tank; accordingly, it is called an inlet or an outlet.

Inlet: A pipe which is connected to fill a tank is known as an inlet.

Outlet: A pipe which is connected to empty a tank is known as an outlet.

Problems on pipes and cisterns are similar to problems on time and work. In pipes and cistern problems, the amount of work done is the part of the tank of filled or emptied. And, the time taken to do a piece of work is the time take to fill or empty a tank completely or to a desired level.


Points to remember:

1) If an inlet connected to a tank fills it in X hours, part of the tank filled in one hour is = 1/X

2) If an outlet connected to a tank empties it in Y hours, part of the tank emptied in one hour is = 1/Y

3) An inlet can fill a tank in X hours and an outlet can empty the same tank in Y hours. If both the pipes are opened at the same time and Y > X, the net part of the tank filled in one hour is given by;

Aptitude Pipesncisterns3

Therefore, when both the pipes are open the time taken to fill the whole tank is given by;

Aptitude Pipesncisterns4

If X is greater than Y, more water is flowing out of the tank than flowing into the tank. And, the net part of the tank emptied in one hour is given by;

Aptitude Pipesncisterns5

Therefore, when both the pipes are open the time taken to empty the full tank is given by;

Aptitude Pipesncisterns6

4) An inlet can fill a tank in X hours and another inlet can fill the same tank in Y hours. If both the inlets are opened at the same time, the net part of the tank filled in one hour is given by;

Aptitude Pipesncisterns7

Therefore, the time taken to fill the whole tank is given by;

Aptitude Pipesncisterns8

In a similar way, If an outlet can empty a tank in X hours and another outlet can empty the same tank in Y hours, the part of the tank emptied in one hour when both the pipes start working together is given by;

Aptitude Pipesncisterns9

Therefore, the time taken to empty the full tank is given by;

Aptitude Pipesncisterns10

5) Three inlets A, B, and C can fill a tank in X, Y and Z hours respectively. If all the inlets are opened together, the time taken to fill the tank is given by;

Aptitude Pipesncisterns11

6) Two pipes can fill a tank in X and Y hours respectively and an outlet can empty the same tank in Z hours. If all the pipes are opened together, part of the tank filled in one hour is given by;

Aptitude Pipesncisterns12

∴ Time taken to fill the tank completely when all the pipes are working is given by;

= Aptitude Pipesncisterns12

7) A pipe can fill a tank in X hours but due to a leak in the bottom, it can be filled in Y hours. The time taken by the leak to empty the tank is given by;

= Aptitude Pipesncisterns12

8) An inlet A is X times faster than inlet B and takes Y minutes less than the inlet B, time taken to fill a tank when both the pipes are opened together is given by;

= Aptitude Pipesncisterns12

And, A alone will fill the tank in Aptitude Pipesncisterns12 minitues

And, B alone will fill the tank in Aptitude Pipesncisterns12 minitues


Aptitude Pipes and Cisterns Test Paper 1
Aptitude Pipes and Cisterns Test Paper 2
Aptitude Pipes and Cisterns Test Paper 3





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