Pipes 'A' and 'B' have the capacity to fill a tank in 12 hours and 15 hours, respectively. Conversely, pipe 'C' can drain the same tank in 20 hours. Initially, when the tank is empty, pipes 'A' and 'C' are turned on simultaneously and left running for 25 hours. Following this, pipe 'B' alone is used to complete the filling of the tank. Calculate the total duration required to fill the tank using this approach.
Let the total capacity of the tank be 60 units Efficiency of pipe ‘A’ = 60/12 = 5 units/hour Efficiency of pipe ‘B’ = 60/15 = 4 units/hour Efficiency of pipe ‘C’ = 60/20 = 3 units/hour Tank filled by pipe ‘A’ and pipe ‘C’ in 25 hours = 25 × (5 – 3) = 50 units Time taken by pipe ‘B’ to fill the remaining tank = (60 – 50)/4 = 2.5 hours Therefore, total time taken to fill the tank = 25 + 2.5 = 27.5 hours Hence, option a.
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