Two pipes can fill a tank in $5$ and $10$ minutes respectively and a waste pipe can empty $4$ gallons per minute. All the three pipes working together can fill the tank in $20$ minutes. The capacity of the tank is:

12

gallons

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10

gallons

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16

gallons

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14

gallons

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Solution

The correct option is D $16$ gallons
Let, pipe A fill the tank $=$ $5$ min
pipe B fill the tank $=$ $10$ min
pipe C empty water $=$ $4$ gallons/min
All pipes together fill the blank $= 20$ min
work done by the waste pipe in $1$ minute = $\frac{1}{20} - (\frac{1}{5} + \frac{1}{10})$
$=$ $\frac{1}{20} - \frac{3}{10}$
$=$ $- \frac{5}{20} = - \frac{1}{4}$
Negative sign means emptying
$∴$ Volume of $\frac{1}{4}$ part $=$ $4$ gallons
$∴$ Total capacity of tank = $4 \times 4 = 16$ gallons

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Two pipes can fill a tank in 5 and 10 minutes respectively and a waste pipe can empty 4 gallons per minute. All the three pipes working together can fill the tank in 20 minutes. The capacity of the tank is:

Two pipes can fill a tank in $5$ and $10$ minutes respectively and a waste pipe can empty $4$ gallons per minute. All the three pipes working together can fill the tank in $20$ minutes. The capacity of the tank is: