Two pipes can fill a tank in $20$ and $24$ minutes respectively and a waste pipe can empty $3$ gallons per minute. All the three pipes working together can fill the tank in $15$ minutes. The capacity of the tank is :

60 g a l l o n s

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100 g a l l o n s

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120 g a l l o n s

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180 g a l l o n s

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Solution

The correct option is C $120 g a l l o n s$
According to given question,

Two ppes can fill atank $= 20 a n d 24 min .$

A waste pipe can empty $= 3 g a l l o n / min .$

Three pipes working $= 15 min .$

So, According to given question,

Work done by the waste pipe in 1 minute

$= \frac{1}{15} - (\frac{1}{20} + \frac{1}{24})$

$= \frac{1}{15} - \frac{11}{120}$

$= - \frac{1}{40}$

Note:- negative sign means emptying

Then,

Volume of $\frac{1}{40} p a r t$ $= 3 g a l l o n s .$

Volume of whole $= 3 \times 40 = 120 g a l l o n s .$

Hence, this is the answer.

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Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is :

Two pipes can fill a tank in $20$ and $24$ minutes respectively and a waste pipe can empty $3$ gallons per minute. All the three pipes working together can fill the tank in $15$ minutes. The capacity of the tank is :