Two pipes A and B can fill a cistern in 37 \(\frac{1}{2}\) minutes and 45 m

Question

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:

Options:

A . 5 min.

B . 9 min

C . 10 min.

D . 15 min.

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.

So, \(x\left(\frac{2}{75}+\frac{1}{45}\right)+(30-x).\frac{2}{75}=1\)

\(\frac{11x}{225}+\frac{(60-2x)}{75}=1\)

11x + 180 - 6x = 225.

x = 9.

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