# Pipes and Cisterns

Pratice Pipes and Cisterns Questions and answers.

Rule Description
1

If a pipe can fill a tank in x hours, then the part filled in 1 hour = $\frac{1}{x}$

2

If a pipe can empty a tank in y hours, then the part of the full tank emptied in 1 hour = $\frac{1}{y}$

3

If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours, then

• The net part filled in 1 hour, When both the pipes are opened =
$\frac{1}{x}-\frac{1}{y}$
• Time taken to fill the tank, when both the pipes are opened =
$\frac{xy}{y-x}$
4

If a pipe can fills or empties tank in x hours and another can fill or empties the same tank in y hours, then time taken to fill or empty the tank, when both pipes are opened =

$\frac{xy}{y+x}$

5

If a pipe fills a tank in x hours and another fills the same tank is y hours, but a third one empties the full tank in z hours, and all of them are opened together, then

• Net part filled in 1 hr =
$\left[\frac{1}{x}+\frac{1}{y}-\frac{1}{z}\right]$
• Time taken to fill the tank =
$\left[\frac{xyz}{-xy+yz+zx}\right]$
6

A pipe can fill a tank in x hrs. Due to a leak in the bottom it is filled in y hrs. If the tank is full, then

Time taken by the leak to empty the tank =

$\frac{xy}{y-x}$ hrs.

7

A cistern has a leak which can empty it in X hours. A pipe which admits Y litres of water per hour into the cistern is turned on and now the cistern is emptied in Z hours. Then

The capacity of the cistern =

$\frac{x+y+z}{z-x}$ litres.

8

Two filling pipes A and B opened together can fill a cistern in t minutes. If the first filling pipe A alone takes X minutes more or less than t and the second fill pipe B along takes Y minutes more or less than t minutes, then

$t=\sqrt{xy}$ minutes.

9

If one filling pipe A is n times faster and takes X minutes less time than the other filling pipe B, then the time they will take to fill a cistern,

• By both the pipes when opened together =
$\left[\frac{nX}{\left(n^2-1\right)}\right]$ minutes.
• Pipe A will fill the cistern in time =
$\left[\frac{X}{\left(n-1\right)}\right]$ minutes.
• Pipe B will fill the cistern in time =
$\left[\frac{nX}{\left(n-1\right)}\right]$ minutes.
10

A cistern is filled by three pipes whose diameters are X cm, Y cm, and Z cm. respectively (where X <Y <Z). Three pipes are running together. If the largest pipe Z alone will fill it in P minutes and the amount of water flowing in by each pipe is proportional to the square of its diameter, then the time in which the cistern will be filled by the three pipes is =

$\left[\frac{pz^2}{x^2+y^2+z^2}\right]$ minutes.