Moderate Time and Work Solved QuestionAptitude Discussion

 Q. A pump can be used either to fill or to empty a tank. The capacity of the tank is (3600text{ m}^3). The emptying capacity of the pump is (10 text{ m}^3/text{min}) higher than its filling capacity. What is the emptying capacity of the pump if the pump needs 12 more minutes to fill the tank than to empty it?
 ✖ A. $10 \text{ m}^3/\text{min}$ ✔ B. $60 \text{ m}^3/\text{min}$ ✖ C. $45 \text{ m}^3/\text{min}$ ✖ D. $90 \text{ m}^3/\text{min}$

Solution:
Option(B) is correct

Let f  $\text m^3/\text{min}$ be the filling capacity of the pump.

Therefore, the emptying capacity of the pump will be = $f+10$ $\text m^3/\text{min}$

The time taken to fill the tank will be = $\dfrac{3600}{f}$ minutes

And the time taken to empty the tank will be = $\dfrac{3600}{f+10}$

We know that it takes 12 more minutes to fill the tank than to empty it

$\dfrac{3600}{f}-\dfrac{3600}{f+10}=12$

$3600f+36000-3600f=12(f^2+10f)$

$f^2+10f-3000=0$

Solving for positive value of $f$ we get, $f=50$

Therefore, the emptying capacity of the pump = $50+10=60$  $\text m^3/\text{min}$.