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 10 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 = 240 units (LCM of 12, 16 and 10) Efficiency of pipe M = 240/12 = 20 units/hr Efficiency of pipe N = 240/16 = 15 units/hr Efficiency of pipe P = 240/-10 = -24 units/hr Capacity of tank filled by pipe M in 6 hours = 6 × 20 = 120 units Capacity of tank emptied by pipe P in 3 hours = -9 × 24 = -72 units Capacity of tank left for pipe N = 240 – 120 – (-72) = 192 units Time taken by pipe N to fill the remaining tank = 192/15 = 12.8 hrs Total time taken = 6 + 3 + 12.8 = 21.8 hrs
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