A booster pump can be used for filling as well as for emptying a tank. The capacity of the tank is 2400 m3 . The emptying capacity of the tank is 10 m3 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?

Q: A booster pump can be used for filling as well as for emptying a tank. The capacity of the tank is 2400 m3 . The emptying capacity of the tank is 10 m3 per minute higher than its filling capacity and the pump needs 8 minutes lesser to empty the tank…

Let the filling capacity of the pump be x m 3 /min. Then, emptying capacity of the pump=(x+10) m 3 /min. so, 2400 x - 2400 x + 10 = 8 ⇔ x 2 + 10 x - 3000 = 0 ⇒ x - 50 + x + 60 = 0 ⇔ x = 50

50 m^3/min
60 m^3/min
72 m^3/min
None of these

Correct Answer: 50 m^3/min

Explanation:

Let the filling capacity of the pump be x $m 3$ /min.

Then, emptying capacity of the pump=(x+10) $m 3$ /min.

so, $\frac{2400}{x} - \frac{2400}{x} = 8 \Leftrightarrow x 2 + 10 x - 3000 = 0$

$\Rightarrow x - 50 + x + 60 = 0 \Leftrightarrow x = 50$

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