Pipes and Cistern Basic Examples

In this class, We discuss Pipes and Cistern Basic Examples.

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Example 1:

A tap can fill a tank in 4 hours. At the same time, We can empty the tank with another tap in 9 hours.

If both the taps opened simultaneously, how much time will it take to fill the tank?

Solution:

In flow filled in 4 hours.

The part of the tank filled in one hour = 1/4

Outflow emptied in 9 hours.

The part of the tank emptied in one hour = 1/9.

Net part filled in one hour = 1/4 – 1/9.= 5/36.

Tank filled in 36/5 hours = 7.2 hours.

Important:

1/x part filled in one hour.

x hours needed to fill.

Example 2:

Two pipes can fill a tank in 10 and 12 hours, respectively. A third pipe can empty the full tank in 20 hours.

If all the pipes operate simultaneously, how much time will it take to fill the tank?

Solution:

Pipe A takes 10 hours to fill the tank

Pipe B takes 12 hours to fill the tank.

(A + B) one hour capacity = (1/10 + 1/12)

Pipe C can empty the tank in 20 hours.

C’s one-hour empty capacity = 1/20

All pipes work simultaneously.

Net part filled in one hour = ((1/10 + 1/12) – 1/20) = 2/15

The tank will be full in 15/2 hours.

= 7.5 hours.