Pipe and Cisterns

Pipes/Taps are used for filling (and emptying) cisterns/tanks with liquid.

• Inlet - A pipe that fills a tank or a cistern or a reservoir. It does ‘plus/positive’ type of work.

• Outlet - A pipe that empties a tank or a cistern or a reservoir. It does ‘minus/negative’ type of work.

Net Work Done = Sum of work done by inlets - Sum of work done by outlets

Work done by a pipe

If a pipe can fill or empty a tank is x hours, then

Part of the tank filled or emptied in 1 hour = 1/x (it’s the work done by the pipe)

Combined work done by two pipes

Here many cases may arise, depending on whether the given pipes are inlet or outlet pipes.

Let us consider two broad cases.

Case 1: Two inlet pipes

If a pipe can fill a tank in x hours & another pipe can fill the tank in y hours (where y > x), then

Work done by pipes per hour (i.e. their efficiency) will be 1/x and 1/y

Their combined efficiency = 1/x + 1/y = (x + y)/xy

This is the part of the tank filled in 1 hour, if both the pipes are opened together.

So, time taken to fill the tank when both pipes are filling it = xy/(x + y)

Case 2: One inlet and One outlet pipe

If a pipe can fill a tank in x hours & another pipe can empty the tank in y hours, then on opening both the pipes,

the net part filled in 1 hour = 1/x – 1/y = (y - x)/xy
(where y > x)
So, time taken to fill the tank when both pipes are working = xy/(y - x)

the net part emptied in 1 hour = 1/y – 1/x = (x - y)/xy
(where x > y)
So, time taken to fill the tank when both pipes are working = xy/(x - y)

Q. Pipes A and B can fill a tank in 12 and 18 minutes respectively. How long will it take for the tank to be filled, if both the pipes are opened together?

Explanations :
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