A pump can be used for filling as well as emptying a tank. The capacity of the tank is 1,500 m 3. The emptying capacity of the tank is 10 m 3 per minute higher than its filling capacity and the pump needs 5 minutes less to empty the tank than it needs to fill it. What is the emptying capacity of the tank?

1m^3=1000 lit so the capacity of the tank is 15x10^5 litre.
Let the pump takes X minutes to completely fill the tank then the rate of filling=( 15x10^5)/X Lit/min
So the emptying rate is= ( 15x10^5)/X +10x10^3 Lit/min =10^4 ( 150/X +1)

Now as per the given info the pump needs 5 minutes less to empty the tank than it needs to fill it.
so {15x 10^5} / { 10^4 ( 150/X +1)} = x-5
solve the equation to find X=30 MIN
so the emptying rate is 60000blit/min or 60 m^3 /min and the tank be emptied in 25 mins

Let the filling capacity of the pump be x => emptying capacity is x+10
$$\frac{1500}{x} - \frac{1500}{x+10}$$ = 5
=> $$1500*\frac{10}{x^2+10x}$$ = 5
=> $$x^2+10x-3000 = 0$$
=> (x+60)(x-50) = 0
=> x = 50
=> Filling capacity is $$50m^3$$ and emptying capacity is $$60m^3$$