Pipes A and B can fill an empty cistern in 15 minutes and 25 minutes respectively. The cistern is empty and both pipes are opened together. After some time pipe B is closed, while pipe A stays open, and the cistern is full exactly 12 minutes after the start. After how many minutes was pipe B closed?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 5 minutes
Pipe A is open for the whole 12 minutes, so its share of the filling is known. Pipe B fills the part that is left.
A in 12 minutes fills \(\displaystyle \frac{12}{15}=\frac{4}{5}\) of the cistern
Part filled by B \(\displaystyle =1-\frac{4}{5}=\frac{1}{5}\)
B fills \(\frac{1}{25}\) per minute, so it was open for \(\displaystyle \frac{1}{5}\times25=5\) minutes
Pipe B was closed after 5 minutes.