Short Cuts: Pipes and Cisterns

Short Cuts: Pipes and Cisterns

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Short Cut: 1

If a pipe fills the tank in x hours, and another fills the same tank in y hours and the third fills the tank in z hour. Then the time required, if all the three pipes are open together to fill the tank is:

Example:

Three pipes can fill the tank in 20, 30 and 40 hours respectively. Find the time required to fill the tank if all the pipes are filled simultaneously.

Solution

Here; x= 20, y= 30 and z= 40 hours

Putting the values in

We get answer= 17.14 hours

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Short Cut: 2

If pipe A can fill a tank in x minutes, pipe B can fill the same in y minutes, there is also an outlet C in the Tank. All these are opened simultaneously and the tank takes “T” minutes to get filled. The time in which C can empty the tank in minutes is given by:

Example:

Two pipes can fill a cistern in 60 minutes and 75 minutes respectively. There is also an outlet C, if all the three pipes are opened together, the tanks get filled in 50 minutes. Find the time taken by C to empty the full tank?

Answer:

Here, x= 60, y= 75 and T= 50 minutes, putting the values in equation:

Answer= 100 minutes

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Short Cut 3

A tap M can empty a tank in x minutes, while another tap N can empty it in y minutes. If both the emptying taps are opened together, then the time taken to empty the full tank is:

Example

A tap can empty the tank in 10 minutes; another tap can do the same in 5 minutes. Find the time required by both the taps to empty the tank simultaneously?

Solution

Here x= 10 and y= 5, putting the values we get:

Answer= 3.33 minutes

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 Pipes and Cisterns important facts and formulae

1. Inlet:

A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as an inlet.

2. Outlet:

A pipe connected with a tank or cistern or reservoir, emptying it, is known as an outlet.

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

part filled in 1 hour =1/x

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

part emptied in 1 hour =1/y

5. 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/x−1/y
6. 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 emptied in 1 hour = 1/y−1/x