Question
A tank has two inlet pipes, A and B, and one outlet
pipe, C. Pipe A can fill the tank in 6 hours, and pipe B can fill the tank in 8 hours. Pipe C can empty the tank in 12 hours. If all three pipes are opened simultaneously, how long will it take to fill the tank completely?Solution
Work done by Pipe A in 1 hour = 1/6 Work done by Pipe B in 1 hour = 1/8 Work done by Pipe C in 1 hour = -1/12 (negative because it empties the tank) Net work done in 1 hour = (1/6) + (1/8) - (1/12) = (4/24) + (3/24) - (2/24) = 5/24 Time to fill the tank = 1 / (5/24) = 24/5 = 4.8 hours = 4 hours 48 minutes Correct Option: b
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