Pipes X and Y can fill an empty cistern in 24 minutes and 40 minutes respectively. The cistern is empty and both pipes are opened together. After some time pipe Y is closed, while pipe X stays open, and the cistern is full exactly 18 minutes after the start. After how many minutes was pipe Y closed?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 10 minutes
Pipe X is open for the whole 18 minutes; pipe Y fills only the part that X leaves.
X fills in 18 minutes \(\displaystyle =\frac{18}{24}=\frac{3}{4}\) of the cistern
Y must fill \(\displaystyle 1-\frac{3}{4}=\frac{1}{4}\) of the cistern
Y fills \(\frac{1}{40}\) per minute, so it needs \(\displaystyle \frac{1}{4}\times40=10\) minutes
Pipe Y was closed after 10 minutes.