A pump can fill a water tank in 4 hours but because of the leakage in the tank it took \( 4\displaystyle\frac{1}{4} \) hours to fill the tank. How much time will it take for the leakage to drain all the water of the full tank?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 68 hours
Consider the part of the tank filled per hour. The pump fills \( \frac{1}{4} \); with the leak the tank fills in \( \frac{17}{4} \) hours, that is \( \frac{4}{17} \) per hour.
\( \displaystyle \text{Leak per hour}=\frac{1}{4}-\frac{4}{17} \)
\( \displaystyle =\frac{17-16}{68}=\frac{1}{68} \)
So the leak empties the full tank in 68 hours.