Question

A pump can fill a tank with water in 2 hours. Because of a leak, it took 3 hours to fill the tank. The leak can drain all the water of the tank in:

• A. 4 hours
• B. 6 hours
• C. 2 hours
• D. 3 hours

Answer 1

The correct option is B 6 hours

Let the volume of the tank be $v$ litres.

Now, the tank can be filled by a pump in 2 hours, then, it can fill $\frac{v}{2}$ in 1 hour

Similarly, the tank can be filled with leakage in 3 hours, then, with a leak, the pump can fill $\frac{v}{3}$ in 1 hour.

Thus, the work done by leakage is $\frac{v}{2}-\frac{v}{3}$ in 1 hour.

$=\frac{v}{6}$

Thus the tank will v litres as volume can be completely emptied by the leakage in $6$ hours.