Question

A tap which allows water at 6 litres / min into a tank is opened. the tank which was initially empty has a leak at its bottom which can empty it in 8 hours. the tank was emptied in 12 hours. find the capacity of the tank.

Answer 1

Let the tap alone fill the tank in x hrs. Then,
$\frac{1}{x} - \frac{1}{8} = \frac{1}{12} \\ x = \frac{8 \times 12}{8 + 12} = \frac{24}{5} \: hrs$
In 1 min, the tap fill 6 L in the tank
Therefore, in 24/5 hrs, the tap fill
6 × 60 × 24/5 = 1728 L is the capacity of tank