Question
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.Solution
Let the total capacity of the tank be 60 units Efficiency of pipe βAβ = 60/12 = 5 units/hour Efficiency of pipe βBβ = 60/15 = 4 units/hour Efficiency of pipe βCβ = 60/20 = 3 units/hour Tank filled by pipe βAβ and pipe βCβ in 25 hours = 25 Γ (5 β 3) = 50 units Time taken by pipe βBβ to fill the remaining tank = (60 β 50)/4 = 2.5 hours Therefore, total time taken to fill the tank = 25 + 2.5 = 27.5 hours Hence, option a.Β
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