Two pipes can fill an empty tank separately in $24$ minutes and $40$ minutes respectively and a third pipe can empty $30$ gallons of water per minute. If all the three pipes are open, empty tanks becomes full in one hour. The capacity of tank (in gallons) is

500

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550

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600

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700

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Solution

The correct option is C $600$
Work done by two pipes individually is $\frac{1}{24}$ and $\frac{1}{40}$ respectively
work done by all three pipe together is $\frac{1}{60}$
Work done by third pipe to empty tha tank $= \frac{1}{60} - (\frac{1}{24} + \frac{1}{40})$
$= \frac{1}{60} - \frac{8}{120}$
$= - \frac{1}{20}$ [-ve sign means emptying]
$∴$ Volume of $\frac{1}{20}$ part $= 30$ gallons
$∴$ Volume of whole tank $= 30 \times 20 = 600$ gallons
Answer is $600$ gallons.

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Two pipes can fill an empty tank separately in 24 minutes and 40 minutes respectively and a third pipe can empty 30 gallons of water per minute. If all the three pipes are open, empty tanks becomes full in one hour. The capacity of tank (in gallons) is

Two pipes can fill an empty tank separately in $24$ minutes and $40$ minutes respectively and a third pipe can empty $30$ gallons of water per minute. If all the three pipes are open, empty tanks becomes full in one hour. The capacity of tank (in gallons) is