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:

5 min.

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9 min.

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10 min.

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15 min.

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Solution

The correct option is B 9 min.
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.
$∴ x (\frac{2}{75} + \frac{1}{45}) + (30 - x) \times \frac{2}{75} = 1$
$\Rightarrow \frac{11 x}{225} + \frac{(60 - x)}{75} = 1$
$\Rightarrow 11 x + 180 - 6 x = 225$
$\Rightarrow x = 9.$

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