# Formulas To Solve Pipes & Cisterns

## Definition & Formula for  Pipes & Cisterns

A pipe is connected to a tank or cistern to fill or empty the tank or cistern
•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.

In pipes and cisterns problems – we need to find out what portion of the tank each of the pipes fill or drain in unit time (say in a minute / hour / second) and then perform arithmetic operation on this value.

## Formula

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

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

3. If pipe A can fill a tank in x hours

Pipe B can empty the full tank in y hours (where y > x),
Then, on opening both the pipes, the net part filled in one hour
= 1/x – 1/y OR xy/y-x hours

4. If pipe A can fill a tank in x hours
Pipe B can empty the full tank in y hours (where x > y),
Then, on opening both the pipes, the net part filled in one hour
= 1/y – 1/x OR yx/x-y hours

5. If pipe A can empty a tank in X hours
Pipe B can empty the same tank in Y hours,
Then part of the tank emptied in one hour when both the pipes start working together
= 1/x + 1/y 