Question

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

• A. $50$ $m^3/min.$
• B. $60$ $m^3/min.$
• C. $72$ $m^3/min.$
• D. None of these

Answer 1

Answer: (A)

$50$ $m^3/min.$

Let the filled capacity of the tank $x{m}^3/minute$

Then emptied capacity of the tank$=(x+10)m^3/minute$

$\therefore \frac{2400}{x}-\frac{2400}{x+10}=8$

$\Rightarrow 2400\left(\frac{10}{x(x+10)}\right)=8$

$\Rightarrow x(x+10)=3000$

$\Rightarrow x=50m^3/min$