A pipe can fill a cistern in 12 minutes and another can fill it in 15 minutes, but a third pipe can empty it in 6 minutes. The first two are kept open for 6 minutes in the beginning and then the third pipe is also opened, in what time will the cistern be emptied?

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Solution

Let the capacity of the tank = LCM of (12,15, 6) = 60 litres.Rate of work done by the first pipe = 60/12 5 L/minRate of work done by the second pipe = 60/15 4L/minRate of work done by the draining pipe = 60/610L/minIf all the pipes are opened simultaneously, (5+4-10) litres will be filled in a minute.Since this comes out to be negative, no water will be filled at any point of time.

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