Pipes A and B can fill an empty cistern in 12 minutes and 16 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 9 minutes after the start. After how many minutes was pipe B closed?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4 minutes
Pipe A is open for the whole 9 minutes, so its share of the filling is known. Pipe B fills the part that is left.
A in 9 minutes fills \(\displaystyle \frac{9}{12}=\frac{3}{4}\) of the cistern
Part filled by B \(\displaystyle =1-\frac{3}{4}=\frac{1}{4}\)
B fills \(\frac{1}{16}\) per minute, so it was open for \(\displaystyle \frac{1}{4}\times16=4\) minutes
Pipe B was closed after 4 minutes.