Pipe A can fill a cistern in $5$ hours and pipe B can fill in $20$ hours. Both Pipe are turned on but there is a leakage in bottom of the cistern. So the cistern is filled in $30$ min. more. In how many time will leakage empty the full cistern ?

Using the net work rate method, pipe A fills one fifth of the cistern per hour and pipe B fills one twentieth per hour, so their combined rate is one quarter per hour. This means the cistern normally fills in 4 hours, but with the leak it takes 30 minutes more, which is 4.5 hours or nine halves of an hour. The combined rate with the leak is therefore one divided by four point five, which equals two ninths per hour. Subtracting the net rate of two ninths from the combined filling rate of one quarter gives a leak rate of one thirty-sixth per hour, meaning the leak empties the full cistern in 36 hours.

• Thanks
• Wrong explanation