Pipe and Cistern problems are similar to time and work problems. A pipe is used to fill or empty the tank or cistern.

Inlet Pipe: A pipe used to fill the tank or cistern is known as Inlet Pipe.

Outlet Pipe: A pipe used to empty the tank or cistern is known as Outlet Pipe.

## Basic Formulas of Pipes and Cisterns

1. If an inlet pipe can fill the tank in x hours, then the part filled in 1 hour = 1/x
2. If an outlet pipe can empty the tank in y hours, then the part of the tank emptied in 1 hour = 1/y
3. If both inlet and outlet valves are kept open, then the net part of the tank filled in 1 hour is

## Shortcut Methods for Pipes and Cisterns

Rule 1: Two pipes can fill (or empty) a cistern in x and y hours while working alone. If both pipes are opened together, then the time taken to fill (or empty) the cistern is given by

Example

Two pipes A and B can fill a cistern in 20 and 30 minutes respectively. If both the pipes are opened together, how long will it take to fill the cistern?
Sol:

Let’s say x = 20 and y = 30

So it will take 12 minutes for both the pipes to full the cistern.

Rule 2: Three pipes can fill (or empty) a cistern in x, y and z hours while working alone. If all the three pipes are opened together, the time taken to fill (or empty) the cistern is given by

Example

Three pipes can fill a tank in 20 minutes, 30 minutes and 40 minutes respectively while working alone. If, all the pipes are opened together, how long will it take to fill the tank full?
Sol:

Let’s say x = 20 minutes, y = 30 minutes, z = 40 minutes

So it will take 9.23 minutes to fill the tank full.

Rule 3: If a pipe can fill a cistern in x hours and another can fill the same cistern in y hours, but a third one can empty the full tank in z hours, and all of them are opened together, then

Example

Two pipes can fill a cistern in 20 minutes and 30 minutes respectively. Third pipe can empty the tank in 40 minutes. If all the three pipes are opened together, how long it will take to fill the tank full?
Sol:

Let’s say x = 20, y = 30 and z = 40

So it will take 17.14 minutes to fill the tank full.

Rule 4: A pipe can fill a cistern in x hours. Because of a leak in the bottom, it is filled in y hours. If it is full, the time taken by the leak to empty the cistern is

Example

A pipe can fill a tank in 3 hours. Because of leak in the bottom, it is filled in 4 hours. If the tank is full, how much time will the leak take to empty it?
Sol:

So leak will empty the tank in 12 hours.
By formula
Let’s say x = 3 and y = 4