Pipes and Cisterns
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
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
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
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
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
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