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in Commercial Mathematics by (49.2k points)
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Two pipes A and B can fill a water tank in 20 minutes and 24 minutes respectively and the third pipe C can empty at the rate of 3 gallons per minute. If A, B and C opened together fill the tank in 15 minutes, the capacity (in gallons) of the tank is 

(a) 180 

(b) 150 

(c) 120 

(d) 60

1 Answer

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Best answer

Part of the tank filled when all the three pipes are opened in 1 minute = \(\frac{1}{15}\)

Part of the tank filled when (A + B) are opened in 1 minute = \(\frac{1}{20}\)+\(\frac{1}{24}\)\(\frac{6+5}{120}\) = \(\frac{11}{120}\)

\(\therefore\) Part of the tank emptied by C in 1 min. = \(\frac{11}{120}\) - \(\frac{1}{15}\) = \(\frac{1}{40}\)

\(\therefore\) Capacity of \(\frac{1}{40}\) part of the tank = 3 gallons

\(\therefore\) Capacity of the tank = (3 × 40) gallons = 120 gallons.

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