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1. Two pipes A and B can fill a cistern in $37 \frac{1}{2}$ 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:

A. 5 min.

B. 9 min.

C. 10 min.

D. 15 min.

Solution:

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{aligned} ∴ x (\frac{2}{75} + \frac{1}{45}) + (30 - x) . \frac{2}{75} = 1 \\ \Rightarrow \frac{11 x}{225} + \frac{60 - 2 x}{75} = 1 \\ \Rightarrow 11 x + 180 - 6 x = 225 \\ \Rightarrow x = 9 \end{aligned}

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