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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Similar questions

34.Two pipes A and B can fill a cistern in 37 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:

Q. Two pipes

A

and

B

can fill a cistern in

37 \frac{1}{2}

minutes and

45 m i n u t e s

respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the

B

is turned off after :

Two pipes A and B can fill a cistern in 37 $\frac{1}{2}$ minutes and 45 minutes respectively. Both pipes are opened simultaneously. After what time should the pipe B be turned off such that the cistern will be filled in half an hour?

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