Question
A tank has two inlet pipes, A and B, which can fill the tank in 6 hours and 8 hours, respectively, and an outlet pipe C, which can empty the tank in 12 hours. If all three pipes are opened together, how long will it take to fill the tank?
Solution
Work done by A in 1 hour = 1/6. Work done by B in 1 hour = 1/8. Work done by C in 1 hour = -1/12. Net work done in 1 hour = (1/6) + (1/8) - (1/12). LCM of 6, 8, and 12 is 24. Net work = (4/24) + (3/24) - (2/24) = 5/24. Time to fill the tank = 24/5 = 4.8 hours. Correct option: b
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