Two pipes, A and B, can fill a cistern in 10 minutes and 12 minutes respectively. Pipe C can empty the cistern in 15 minutes. If all 3 pipes are opened together, how long will it take to fill the cistern completely?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \displaystyle\frac{60}{7} \) minutes
In one minute, pipe A fills \( \frac{1}{10} \) of the cistern, pipe B fills \( \frac{1}{12} \) and pipe C empties \( \frac{1}{15} \). Together, the part filled per minute is
\( \displaystyle \frac{1}{10}+\frac{1}{12}-\frac{1}{15}=\frac{6+5-4}{60} \)
\( \displaystyle =\frac{7}{60} \)
The time taken is the reciprocal of this rate:
\( \displaystyle \text{Time}=\frac{60}{7}\text{ minutes} \)