Pipe A can fill an empty cistern in 50 hours, and pipe B can empty \(\frac{1}{3}\) of the full cistern in 80 hours. Both pipes are opened together when the cistern is empty. After 2 hours, A is closed. How long will B take to empty the cistern after that?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 7.6 hours
A fills faster than B empties, so in the first 2 hours some water collects. After A is closed, B alone has to empty only this water.
B empties \(\frac{1}{3}\) in 80 hours, so it empties the full cistern in \(80\times3=240\) hours
Net filling per hour \(\displaystyle =\frac{1}{50}-\frac{1}{240}=\frac{24-5}{1200}=\frac{19}{1200}\)
Water collected in 2 hours \(\displaystyle =\frac{19}{600}\) of the cistern
Time for B to empty it \(\displaystyle =\frac{19}{600}\times240=7.6\) hours