Question
Two inlet pipes, each with the same capacity, can fill
an empty tank 'A' together in 20 minutes. There is also an outlet pipe that can empty 40% of the tank 'A' in 10 minutes. If we open just one of these inlet pipes and the outlet pipe simultaneously to drain a completely filled tank 'B'—which holds three times the volume of tank 'A'—how long will it take to empty tank 'B'?Solution
Total time taken by outlet pipe to empty the tank 'A' = 10 X (100/40) = 25 minutes Let the capacity of tank 'A' be 100 units (L.C.M. of 20 minutes and 25 minutes) Total efficiency of two inlet pipes = (100/20) = 5 units/minute Efficiency of one inlet pipe = 2.5 units/minute Efficiency of outlet pipe = (100/25) = - 4 units/minute Combined efficiency of one inlet and one outlet pipe = 2.5 - 4 = - 1.5 (' - ' sign denotes efficiency of outlet pipe is more than the inlet pipe) Capacity of tank 'B' = (100 X 3) = 300 units Required time = (300/1.5) = 200 minutes
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