Question
Two inlet pipes M and N alone can fill a tank in 12
hours and 15 hours respectively and an outlet pipe P alone can empty the whole tank in 10 hours. First pipe M is opened for 4 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 = 60 units (LCM of 12, 15 and 10) Efficiency of pipe M = 60/12 = 5 units/hr Efficiency of pipe N = 60/15 = 4 units/hr Efficiency of pipe P = 60/-10 = -6 units/hr Capacity of tank filled by pipe M in 4 hours = 5 × 4 = 20 units Capacity of tank emptied by pipe P in 2 hours = -6 × 2 = -12 units Capacity of tank left for pipe N = 60 – 20 – (-12) = 52 units Time taken by pipe N to fill the remaining tank = 52/4 = 13 hrs Total time taken = 4 + 2 + 13 = 19 hrs
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