A pipe alone can fill an empty tank in 15 hours. A leak at the bottom of the tank lets water out, so the same pipe, opened on the empty tank, now takes 18 hours to fill it. In how many hours can the leak alone empty the full tank?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 90 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 \(\frac{1}{15}\) of the tank in one hour
Pipe with the leak fills \(\frac{1}{18}\) of the tank in one hour
Leak empties \(\displaystyle \frac{1}{15}-\frac{1}{18}=\frac{6-5}{90}=\frac{1}{90}\) of the tank in one hour
The leak alone empties the full tank in 90 hours.