Pipes & 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:
A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as an inlet.

Outlet:
A pipe connected with a tank or cistern or reservoir, emptying it, is known as an outlet.

If a pipe can fill a tank in x hours, then:
part filled in 1 hour = 1/x

If a pipe can empty a tank in y hours, then:
part emptied in 1 hour = 1/y

If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where y > x), then on opening both the pipes, then
the net part filled in 1 hour = 1/x - .1/y

If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where x > y), then on opening both the pipes, then

the net part emptied in 1 hour = 1/y - 1/x .

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
(xy/x+y) hours

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
[xyz/(xy + yz + zx)] hours

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
Net part filed in 1 hour = 1/x + 1/y - 1/z
Time taken to fill full cistern = [xyz/(yz + xz - xy)]

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
xy/(y-x) hours