A pipe can fill a tank in 8 hours and another pipe can empty the full tank in 12 hours. If both pipes are opened together in the empty tank, in how many hours will the tank be full?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 24 hours
In one hour, the first pipe fills \(\frac{1}{8}\) of the tank and the second pipe empties \(\frac{1}{12}\) of it. The net part filled per hour is
\( \displaystyle \frac{1}{8} - \frac{1}{12} = \frac{3 - 2}{24} \)
\( \displaystyle = \frac{1}{24} \)
So the tank is full in 24 hours.
Why the other options are incorrect
Option (1) 4 hours — Incorrect. This is the difference of the two times, \(12 - 8\); times cannot be subtracted, only the parts per hour.
Option (2) 4.8 hours — Incorrect. This treats the second pipe as filling too: \(\frac{1}{8} + \frac{1}{12} = \frac{5}{24}\).
Option (3) 20 hours — Incorrect. In 20 hours the net part filled is only \(\frac{20}{24} = \frac{5}{6}\) of the tank.