Two pipes A and B can fill a cistern in 371/2 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:

Answer: Option B

Let B be turned off after x minutes.
Then, Part filled by (A + B) in x min. + Part filled by A in (30 - x) min. = 1
$$\begin{array}{rl}& \therefore x\left(\frac{2}{75}+\frac{1}{45}\right)+\left(30-x\right).\frac{2}{75}=1\\ & \Rightarrow \frac{11x}{225}+\frac{60-2x}{75}=1\\ & \Rightarrow 11x+180-6x=225\\ & \Rightarrow x=9\end{array}$$