Two pipes A and B can fill a tank in 5 hours and 6 hours respectively. Pipe C can empty it in 12 hours. If all three pipes are opened together, then the time taken to fill the tank is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(3\displaystyle\frac{9}{17}\) hours
In one hour A fills \(\frac{1}{5}\) of the tank, B fills \(\frac{1}{6}\) and C empties \(\frac{1}{12}\). With all three open, the net work per hour is
\( \displaystyle \frac{1}{5} + \frac{1}{6} - \frac{1}{12} \)
\( \displaystyle = \frac{12 + 10 - 5}{60} = \frac{17}{60} \)
So the time to fill the tank is
\( \displaystyle \frac{60}{17} = 3\frac{9}{17} \) hours