Question
A tank has two pipes, Pipe A and Pipe B. Pipe A fills
the tank in 10 hours, while Pipe B fills it in 15 hours. Pipe C can empty the tank in 30 hours. If all three pipes are opened together, how long will it take to fill the tank?Solution
Work done by Pipe A in 1 hour = 1/10. Work done by Pipe B in 1 hour = 1/15. Work done by Pipe C in 1 hour = -1/30. Net work done in 1 hour = 1/10 + 1/15 - 1/30. Finding LCM of 10, 15, and 30 = 30. Net work = (3 + 2 - 1)/30 = 4/30 = 2/15. Time taken to fill the tank = 15/2 = 7.5 hours. Correct Option: b) 7.5 hours
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