Two pipes A and B can fill a cistern in 37$ \dfrac{1}{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:

5 min.

9 min.

10 min.

15 min.

Explanation:

Let B be turned off after $ x $ minutes. Then,

Part filled by $\left(A + B\right)$ in $ x $ min. + Part filled by A in $\left(30 - x \right)$ min. = 1.

$\therefore x \left(\dfrac{2}{75} +\dfrac{1}{45} \right) $+ $\left(30 - x \right)$.$ \dfrac{2}{75} $= 1

$\Rightarrow \dfrac{11x}{225} $+$ \dfrac{(60 -2x)}{75} $= 1

$\Rightarrow$ 11$ x $ + 180 - 6$ x $ = 225.

$\Rightarrow x $ = 9.