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Byju's Answer

Standard VII

Mathematics

Time and Work

A cistern has...

Question

A cistern has two taps which fill it in $12$ minutes and $15$ minutes respectively. There is also a waste pipe in the cistern. When all the pipes are opened, the empty cistern is full in $20$ minutes. How long will the waste pipe take to empty the full cistern?

12

minutes

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10

minutes

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8

minutes

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16

minutes

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Solution

The correct option is B $10$ minutes
Let the waste pipe take $x$ minutes to empty the full cistern. Then,
$(\frac{1}{12} + \frac{1}{15} - \frac{1}{x}) = \frac{1}{20}$

$\Rightarrow \frac{1}{x} = \frac{1}{12} + \frac{1}{15} - \frac{1}{20} = \frac{5 + 4 - 3}{60} = \frac{6}{60} = \frac{1}{10}$

$∴$ The waste pipe takes 10 minutes to empty the full cistern.

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Similar questions

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A cistern has two taps which fill it in 12 minutes and 15 minutes respectively. There is also a waste pipe in the cistern. When all the pipes are opened, the empty cistern is full in 20 minutes. How long will the waste pipe take to empty the full cistern?

The correct option is B 10 minutesLet the waste pipe take x minutes to empty the full cistern. Then, (112+115−1x)=120⇒1x=112+115−120=5+4−360=660=110∴ The waste pipe takes 10 minutes to empty the full cistern.

A cistern has two taps which fill it in $12$ minutes and $15$ minutes respectively. There is also a waste pipe in the cistern. When all the pipes are opened, the empty cistern is full in $20$ minutes. How long will the waste pipe take to empty the full cistern?