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

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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?

posted Jan 26, 2021

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.

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

answer May 9, 2021 by anonymous
There is a small error in your calculation.
If the tap is closed, every 13 (not 11) hours the tank loses 2V/11.

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