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There are three pipes connected to a tank. Two out of the three pipes are filling pipes which can fill a tank in 10 and 15 minutes respectively and third pipe is waste pipe that carries out 6 gallons of liquid per minute. If all three pipes working together fill pipe in 24 minutes then capacity of tank in gallons is?

There are three pipes connected to a tank. Two out of the three pipes are filling pipes which can fill a tank in 10 and 15 minutes respectively and third pipe is waste pipe that carries out 6 gallons of liquid per minute. If all three pipes working together fill pipe in 24 minutes then capacity of tank in gallons is? Correct Answer 48

Let A, B be two filling pipes and C be the waste pipe.

Given that A takes 10 minutes, B takes 15 minutes and A + B + C together take 24 minutes to fill

the tank

∴ let total capacity = LCM = 120

Efficiency of pipe A = E(A) = 120/10 = 12,

Efficiency of pipe B = E(B) = 120/15 = 8

And, efficiency of pipe A, B and C together E (A + B + C) = 120/24 = 5                   

Hence, efficiency of pipe C = E(C) = 5 – 12 – 8 = -15           

According to question,

15 units = 6 gallons

∴ 120 units = (6/15) × 120 = 48 gallons

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