Two pipes A and B can fill a cistern in $30$ min and $40$ min respectively, Both the pipes are turned on simultaneously. When should the second pipe be closed if the cistern is to be filled in $24$ min ?

6

min

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8

min

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10

min

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12

min

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Solution

The correct option is B $8$ min
Let the second pipe be closed after x minutes.
Then, $\frac{24}{30} + \frac{x}{40} = 1$
$\Rightarrow \frac{96 + 3 x}{120} = 1 \Rightarrow 3 x = 120 - 96 = 24 \Rightarrow x = 8 m i n$

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