A crack at the bottom of a cistern can empty it in 3 hours. A fill tap that fills water at the rate of 10 litres/min is turned on when the cistern is full and now it takes 6 hours for the tank to empty. What is the capacity of the tank?

A) 2400 Ltrs.

B) 3600 Ltrs.

C) 1200 Ltrs.

D) 2000 Ltrs.

Correct answer:
B) 3600 Ltrs.

Description for Correct answer:
Let A hours be the time taken by the fill pipe to fill the tank and 8 hours be the time taken for the leak at the bottom of the tank to drain the tank.

Then, \( \Large \frac{1}{A}-\frac{1}{B}=\frac{-1}{6} \).

We know that \( \Large \frac{1}{B}=\frac{1}{3} \) (given)

Or \( \Large \frac{1}{A}-\frac{1}{3}=\frac{-1}{6}\ or\ \frac{1}{A}=\frac{1}{6} \)

Or A = 6 hrs or 360 min.

Capacity of the tank = 10 ltr/min x 360 min = 3600 Itrs.


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