Two pipes can fill a cistern in 8 and 12 hours respectively. The pipes are opened simultaneously, and it takes 12 minutes more to fill the cistern due to leakage. If the cistern is full, what will be the time taken by the leakage to empty it?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 120 hours
Each rate is the part of the cistern filled per hour. Without the leak, the two pipes together fill
\( \displaystyle \frac{1}{8} + \frac{1}{12} = \frac{3 + 2}{24} = \frac{5}{24} \)
of the cistern per hour, so they need
\( \displaystyle \frac{24}{5} \text{ hours} = 4 \text{ hours } 48 \text{ minutes} \)
With the leak it takes 12 minutes more, that is 5 hours, so the net rate is \(\frac{1}{5}\) of the cistern per hour. The leak empties per hour
\( \displaystyle \frac{5}{24} - \frac{1}{5} = \frac{25 - 24}{120} = \frac{1}{120} \)
of the cistern, so it empties a full cistern in 120 hours.
CBSE Applied Mathematics (Class XII):
Pipes and Cisterns
