Question

Two pipes can fill a tank in 12 and 20 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom, 30 minutes extra are taken for the cistern to be filled up. If the cistern is full, in what time would the leak empty it?

Answer 1

Cistern filled by both pipes in one hour = 1/12+1/20=2/15th
Therefore both pipes filled the cistern in 15/2hrs.
Now, due to leakage both pipes filled the cistern in 15/2+30/60=8hrs.
Therefore Due to leakage, filled part in one hour = 1/8
Therefore part of cistern emptied, due to leakage in one hour = 2/15-1/8= 1/120th
In 120 hrs, the leak would empty the cistern.