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 8 hours. First pipe M is opened for 5 hours, then pipe P is opened for 2 hours and rest of the tank is filled by pipe N. In what time will the tank be filled completely?Solution
Total capacity = 120 units (LCM of 10, 12 and 8) Efficiency of pipe M = 120/10 = 12 units/hr Efficiency of pipe N = 120/12 = 10 units/hr Efficiency of pipe P = 120/-8 = -15 units/hr Capacity of tank filled by pipe M in 5 hours = 12 × 5 = 60 units Capacity of tank emptied by pipe P in 2 hours = -15 × 2 = -30 units Capacity of tank left for pipe N = 120 – 60 – (-30) = 90 units Time taken by pipe N to fill the remaining tank = 90/10 = 9 hrs Total time taken = 5 + 2 + 9 = 16 hrs
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