Discussion
A Pump can be operated both for filling and emptying a Tank. If the capacity of the tank is 2400 m\(^{3}\). The emptying capacity of the Pump is 10 m\(^{3}\)/minute higher than its filling capacity, consequently the Pump needs 8 minute less time to empty the Tank than to fill it. Find the filling capacity.
Answer: A
The filling capacity is 3000 m3/hr.
Let the filling rate be \(f\) m3/minute, so emptying is \(f + 10\). Emptying takes 8 minutes less:
\[ \begin{aligned} \frac{2400}{f} - \frac{2400}{f+10} &= 8 \\ 2400 \times 10 &= 8f(f + 10) \\ f^{2} + 10f - 3000 &= 0 \end{aligned} \]
\[ (f + 60)(f - 50) = 0 \Rightarrow f = 50 \]
The pump fills 50 m3 a minute, which is \(50 \times 60 = 3000\) m3 an hour. Check: filling takes 48 minutes and emptying (60 m3/min) takes 40, a difference of 8. The options are in m3 per hour, so the trap is to stop at 50.
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