A booster pump can be used for filling as well as for emptying a tank. The capacity of the tank is 2400 m$$^3$$. The emptying capacity of the tank is 10 m$$^3$$ per minute higher than its filling capacity and the pump needs 8 minutes lesser to empty the tank than it needs to fill it, What is the filling capacity of the pump?

We are given the information that, 
The total capacity of the tank is $$2400m^3$$
The emptying capacity is given to be $$10m^3$$ per minute more than the filling capacity. So, let us consider that the emptying capacity is X+10 and the filling capacity is X. 

We are also given that the filling time is 8 minutes more than emptying time. 

Drawing up the equations, 
$$\frac{2400}{X+10}+8=\frac{2400}{X}$$

$$1=\frac{300}{X}-\frac{300}{X+10}$$

$$1=300\left(\frac{1}{X}-\frac{1}{X+10}\right)$$

$$1=300\left(\frac{10}{X\left(X+10\right)}\right)$$

$$X^2+10X-3000=0$$

$$\left(X+60\right)\left(X-50\right)$$

Since X cannot be negative, X is $$50\ \frac{m^3}{\min}$$

Hence, fillingcapacity is $$50\ \frac{m^3}{\min}$$