Problems on Pipes and Cisterns are same as what we did on Time and Work.

Let us look at some of the important terms, tips and formulas for solving the problems based on Pipes and Cisterns :

Inlet

Inlet may be defined as the pipe connected with a pipe/ cistern\ reservoir that fills it.

Outlet

Outlet may be defined as the pipe connected with a pipe/ cistern\ reservoir that empties it.

1. If a pipe fills a tank in ‘x’ hours, then the pipe fills 1/x of the same tank in 1 hour.

2. If a pipe empties a tank in ‘y’ hours, then the pipe empties 1/y of the same tank in 1 hour.

In many problems, filling the container by inlet is considered as positive work and emptying the container by outlet is considered as negative work.

Let a pipe fill a tank in x hours and another pipe can empty the full tank in y hours. So, part of tank filled in 1 hour, when both pipes are opened.

[math]
\frac{1}{x}\;-\;\frac{1}{y}
[/math]

Let a pipe fill a tank in x hours and another pipe can empty the full tank in y hours. So, part of tank emptied in 1 hour, when both pipes are opened.

[math]
\frac{1}{y}\;-\;\frac{1}{x}
[/math]

Let a pipe fill a tank in x hours while another fills the same tank in y hours but a third one empties the full tank in z hours. If all the three pipes are opened together, then the part of the tank filled in 1 hour :

[math]
\frac{1}{x}\;+\;\frac{1}{y}\;-\;\frac{1}{z}
[/math]