Two inlet pipes can fill a tank in 30 minutes and 24 minutes respectively. An outlet pipe can empty 10 litres of water per minute. If all the three pipes working together can fill the tank in 15 minutes, the capacity of the tank is :

1200 litres

The correct answer is Option (2) → 1200 litres

Rate of pipe 1 = $\frac{1}{30}$ tank per minute

Rate of pipe 2 = $\frac{1}{24}$ tank per minute

Let the capacity of the tank be V L. The outlet pipe's rate,

Rate of outlet pipe = $\frac{10}{V}$ tank per minute

Total rate = $\frac{1}{15}$ tank per minute

∴ Total rate = rate of pipe 1 + rate of pipe 2 - rate of outlet pipe

$=\frac{1}{15}=\frac{1}{30}+\frac{1}{24}-\frac{10}{V}$

$\frac{1}{120}=\frac{10}{V}$

$V=1200L$