A pipe can fill a tank with petrol in 3 hours. Due to leakage, it took \( 4\displaystyle\frac{2}{3} \) hours to fill the tank. How much time will it take for the leakage to drain all the petrol of the full tank?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 8.4 hours
The key quantity is the part of the tank filled or emptied in one hour. Since \( 4\frac{2}{3}=\frac{14}{3} \) hours:
\( \displaystyle \text{Pipe alone}:\ \frac{1}{3}\ \text{per hour} \)
\( \displaystyle \text{Pipe with leak}:\ \frac{1}{14/3}=\frac{3}{14}\ \text{per hour} \)
The leak empties the difference:
\( \displaystyle \text{Leak}=\frac{1}{3}-\frac{3}{14} \)
\( \displaystyle =\frac{14-9}{42}=\frac{5}{42}\ \text{per hour} \)
\( \displaystyle \text{Time for the leak to empty the full tank}=\frac{42}{5} \)
\( \displaystyle =8.4\text{ hours} \)