An inlet pipe fills an empty water tank in 8 hours. An outlet pipe at the bottom of the tank can empty the full tank in 12 hours. The tank is empty and both pipes are opened at the same time. In how many hours will the tank be full?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 24 hours
When both pipes are open, the outlet takes away part of what the inlet puts in, so the tank fills at the difference of the two rates.
Inlet fills \(\frac{1}{8}\) of the tank in an hour
Outlet empties \(\frac{1}{12}\) of the tank in an hour
Net filling in an hour \(\displaystyle =\frac{1}{8}-\frac{1}{12}=\frac{3-2}{24}=\frac{1}{24}\)
The tank is full in 24 hours.
Why the other options are incorrect
Option (1) 4 hours — Incorrect. This is just \(12-8\); times cannot be subtracted, only rates.
Option (2) 4.8 hours — Incorrect. This would be the time if both pipes filled the tank: \(\frac{8\times12}{20}\).
Option (3) 20 hours — Incorrect. This is \(8+12\); in 20 hours the tank is only \(\frac{20}{24}\) full.