Two inlet pipes M and N alone can fill a tank in 15 hours and 18 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 4 hours and rest of the tank is filled by pipe N. In what time will the tank be filled completely?

Solution

Total capacity = 90 units (LCM of 15, 18 and 10) Efficiency of pipe M = 90/15 = 6 units/hr Efficiency of pipe N = 90/18 = 5 units/hr Efficiency of pipe P = 90/-10 = -9 units/hr Capacity of tank filled by pipe M in 6 hours = 6 × 6 = 36 units Capacity of tank emptied by pipe P in 4 hours = -9 × 4 = -36 units Capacity of tank left for pipe N = 90 – 36 – (-36) = 90 units Time taken by pipe N to fill the remaining tank = 90/5 = 18 hrs Total time taken = 6 + 4 + 18 = 28 hrs