A pump can be operated both for filling a tank and for emptying it. The capacity of the tank is 2400 $$m^{3}$$. The emptying capacity of the pump is 10 $$m^{3}$$ per minute higher than its filling capacity. Consequently, the pump needs 8 minutes less to empty the tank as to fill it. The filling capacity of the pump is

Let the filling capacity of pump be "X" $$m^3$$ .
It is given emptying capacity of pump = X + 10 
Total volume of the tank = 2400 

Time taken to fill the tank = $$\dfrac{2400\ }{X}$$

Time taken to empty the tank = $$\dfrac{\ 2400}{X\ +10}$$

Now, it is given that : $$\dfrac{\ 2400}{X\ +10}$$ = $$\dfrac{2400\ }{X}$$ - 8
 
So , this gives $$\dfrac{\ 2400(10)}{X\left(X+10\right)}=8$$

therefore, 3000 = X(X+10)

Hence, X = 50 or X = -60.
But X cannot be negative as it is filling capacity which is +ve.

Therefore, answer will be 50 $$m^3$$