A tap can fill a cistern in 11 hours, but due to .............in what time will the cistern become empty due to leakage?

Question

A tap can fill a cistern in 11 hours, but due to a leakage it took 13 hours to fill the cistern.
If the cistern is full, in what time will the cistern become empty due to leakage?

Answer 1

71.5 hours
.
Let say the tap rate is X L/hour.
Then the leakage rate is (13-11) * X / 13 = 0.154 * X
The cistern capacity = 11 * X
Thus the leakage will empty the cistern in 11 / 0.154 = 71.5 hours.

Answer 2

Let V = volume of the full tank
If the tap is open, The tank is filled at a rate of V/11 l/hr
Now , because of a leak , an extra volume of water is added to the tank. Extra volume = 2 V/11
If the tap is closed, every 11 hours the tank loses 2V/11
then , after 2V/11 x 5 + 1V/11 , the tank is empty
therefore 11 x 5 + 5,5 = 60,5 hours
The answer is 60,5 hours

Comments

There is a small error in your calculation.
If the tap is closed, every 13 (not 11) hours the tank loses 2V/11.