Question
Two pipes A and B can fill a tank in 12 hours and 16
hours, respectively. A third pipe C can empty the tank in 24 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 = 1/12. Work done by B in 1 hour = 1/16. Work done by C in 1 hour = −1/24. Net work done in 1 hour = 1/12 + 1/16 − 1/24. LCM of 12, 16, and 24 is 48. Net work done in 1 hour = (4 + 3 − 2)/48 = 5/48. Time taken to fill the tank = 48/5 = 9.6 hours. Ans. b
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