Two pipes can fill a cistern in 30 and 15 h respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom 5 h extra are taken for cistern to be filled up. If the cistern in full in what time would the leak empty it ?

The rates of the two pipes are 1/30 and 1/15 per hour, giving a combined filling rate of 1/30 + 1/15 = 1/10 per hour. Without a leak, they would take 10 hours, but with the leak taking 5 extra hours, the combined rate with the leak is 1/15 per hour. The leak's rate is the difference between these totals, which is 1/10 - 1/15 = 1/30 per hour, meaning the leak would empty the cistern in 30 hours. The result is 30 hours.

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