A pipe can fill an empty tank in 8 hours. Because of a leak at the bottom of the tank, the same pipe, opened on the empty tank, takes 10 hours to fill it. In how many hours can the leak alone empty the full tank?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 40 hours
With the leak acting, the tank gains the pipe's one-hour work minus the leak's one-hour work. So the leak's share is the difference between the two filling rates.
Pipe alone fills \(\frac{1}{8}\) of the tank in one hour
Pipe with the leak fills \(\frac{1}{10}\) of the tank in one hour
Leak empties \(\displaystyle \frac{1}{8}-\frac{1}{10}=\frac{5-4}{40}=\frac{1}{40}\) of the tank in one hour
The leak alone empties the full tank in 40 hours.