a bath can filled by the cold water pipe in 10 minutes and by the hot water pipe in 15 minutes. a person leaves the bathroom after turning on both pipes simultaneously and returns at the moment when the bath should be full. Finding ,however,that the waste pipe has been opened he now closes it. in 4 minutes more, bath is full. in what time would be the waste pipe empty it?

The time taken when only C and H are on, is (10*15)/(10+15) = 6 min

At the after the waste pipe was closed the two taps C and H were on for 4 min, so filled part is 4/6

This 4/6 part should have been completed, if the waste pipe wasn't on before, so it did the work of emptying 4/6 part

So in 6 min  - 4/6 part was emptied

so (6*6)/4    -  part (total part) will be emptied

It will take 9 minutes.