Question
Two inlet pipes M and N alone can fill a tank in 10
hours and 12 hours respectively and an outlet pipe P alone can empty the whole tank in 5 hours. First pipe M is opened for 6 hours, then pipe P is opened for 3 hours and rest of the tank is filled by pipe N. In what time will the tank be filled completely?Solution
Total capacity = 60 units (LCM of 10, 12 and 5) Efficiency of pipe M = 60/10 = 6 units/hr Efficiency of pipe N = 60/12 = 5 units/hr Efficiency of pipe P = 60/-5 = -12 units/hr Capacity of tank filled by pipe M in 6 hours = 6 × 6 = 36 units Capacity of tank emptied by pipe P in 3 hours = -12 × 3 = -36 units Capacity of tank left for pipe N = 60 – 36 – (-36) = 60 units Time taken by pipe N to fill the remaining tank = 60/5 = 12 hrs Total time taken = 6 + 3 + 12 = 21 hrs
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