Pipes ‘A’ and ‘B’ can fill a tank in 6 hours and 8 hours, respectively and pipe ‘C’ can empty the full tank in 12 hours. All three pipes are opened together, but after 2 hours pipe ‘B’ is closed while pipes ‘A’ and ‘C’ are opened until the tank is full. How many hours will the empty tank be filled this way?

Solution

Let the capacity of the tank be (L.C.M of 6, 8, and 12) = 24 units Efficiency of pipe ‘A’ = 24/6 = 4 units/hour Efficiency of ‘B’ = 24/8 = 3 units/hour Efficiency of ‘C’ = 24/12 = 2 units/hour Effective efficiency of (A + B – C) = 4 + 3 – 2 = 5units/hour In 2 hours, part of the tank will be filled = 5 × 2= 10 units Remaining part = 24 -10 = 14 units time taken to fill the remaining part of the tank by A and C = 14/2=7 Total timing =2+7 =9hours