# Pipes and Cisterns

Problems on Pipes and Cisterns are based on the basic concept of time and work. Pipes are connected to a tank or cistern and are used to fill or empty the tank or cistern. In pipe and cistern, the work is done in form of filling or emptying a cistern/tank.

## Important Facts & Formulae

1. 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.

2. If a pipe can fill a tank in x hours, then:

 part filled in 1 hour = 1 . x

3. If a pipe can empty a tank in y hours, then:

 part emptied in 1 hour = 1 . y

4. 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 - 1 . x y

5. 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 - 1 . y x

## TIPS on cracking Aptitude Questions on Pipes and Cisterns

Assume that the filling rate or the emptying rate for each pipe is constant

1.   Question: Pipe A can fill the tank in 20 hours while Pipe B alone can fill it in 30 hours and Pipe C can empty the tank in 40 hours. If all the pipes are opened together, in how long will the tank be full?

Solution:

Let the capacity of the tank be C liters

Fill rate of A, Fa = C/20 liters per hr

Fill rate of B, Fb = C/30 liters per hr

Fill rate of C, Fc = - C/40 liters per hr [Negative since this pipe is emptying the tank]

Let t be the time taken to fill the tank to maximum capacity.

t x [Fa + Fb + Fc] = C => t = 120/7 hrs

2.    Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 2.5 hours to fill the tank. If the pump is turned off, how long will it take to empty the tank?

Solution:

Fill rate of pipe, Fp = C/2 liters per hr

Let the fill rate of the leak be FL

2.5 x [Fp + FL] = C => FL = - C/10

With the pump turned off, it would take 10 hrs for the leak to empty the tank.

Note: The problems on Pipes and Cisterns are much alike those on Time and Work so it is easy to draw analogy from them and can be solved following similar procedure. Time taken to fill/empty a cistern is equivalent to time taken to do a work. Different pipes are equivalent to the different workers.