Question

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 than to fill it. Find the filling capacity of the pump.

• A. \(50\) m\(^3\)/min
• B. \(56\) m\(^3\)/min
• C. \(55\) m\(^3\)/min
• D. \(52\) m\(^3\)/min
• E. \(54\) m\(^3\)/min

Answer 1

The Correct Option is A

Concept: \[ \text{Time} = \frac{\text{Work}}{\text{Rate}} \]
Step 1: Let filling rate = \(x\).
\[ \text{Emptying rate} = x + 10 \]
Step 2: Form equation.
\[ \frac{2400}{x} - \frac{2400}{x+10} = 8 \]
Step 3: Solve.
\[ 2400 \left(\frac{1}{x} - \frac{1}{x+10}\right) = 8 \] \[ 2400 \cdot \frac{10}{x(x+10)} = 8 \] \[ \frac{24000}{x(x+10)} = 8 \] \[ x(x+10) = 3000 \] \[ x^2 + 10x - 3000 = 0 \] \[ (x+60)(x-50) = 0 \Rightarrow x = 50 \]
Step 4: Option analysis.

• (A) Correct \checkmark
• Others incorrect $\times$

Conclusion:
Thus, the correct answer is
Option (A).