Two pipes A and B can fill a cistern in $37 \frac{1}{2}$ min and $45$ min respectively. Both pipes were opened and the cistern was filled in just $\frac{1}{2}$ an hour if the pipe B is turned off after what time it is opened?

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 C $9$ 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.
$∴ x (\frac{2}{75} + \frac{1}{45}) + (30 - x) \frac{2}{75} = 1$
$\Rightarrow \frac{11 x}{225} + \frac{60 - 2 x}{75} = 1$
$\Rightarrow 11 x + 180 - 6 x = 225$
$\Rightarrow 5 x = 225 - 180$
$\Rightarrow 5 x = 45$
$\Rightarrow x = 9$

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A

and

B

can fill a cistern in

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minutes and

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

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Two pipes A and B can fill a cistern in 3712 min and 45 min respectively. Both pipes were opened and the cistern was filled in just 12 an hour if the pipe B is turned off after what time it is opened?

The correct option is C 9 minLet 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(275+145)+(30−x)275=1 ⇒11x225+60−2x75=1 ⇒11x+180−6x=225 ⇒5x=225−180 ⇒5x=45 ⇒x=9

Two pipes A and B can fill a cistern in $37 \frac{1}{2}$ min and $45$ min respectively. Both pipes were opened and the cistern was filled in just $\frac{1}{2}$ an hour if the pipe B is turned off after what time it is opened?