Question
Two inlet pipes M and N alone can fill a tank in 12
hours and 16 hours respectively and an outlet pipe P alone can empty the whole tank in 8 hours. First pipe M is opened for 6 hours, then pipe P is opened for 4 hours and rest of the tank is filled by pipe N. In what time will the tank be filled completely?Solution
Total capacity = 48 units (LCM of 12, 16 and 8) Efficiency of pipe M = 48/12 = 4 units/hr Efficiency of pipe N = 48/16 = 3 units/hr Efficiency of pipe P = 48/-8 = -6 units/hr Capacity of tank filled by pipe M in 6 hours = 6 × 4 = 24 units Capacity of tank emptied by pipe P in 4 hours = -6 × 4 = -24 units Capacity of tank left for pipe N = 48 – 24 – (-24) = 48 units Time taken by pipe N to fill the remaining tank = 48/3 = 16 hrs Total time taken = 6 + 4 + 16 = 26 hrs
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