Question
Pipe βAβ takes 25 minutes to fill a tank. Pipe βBβ takes 30 minutes to empty the same tank. If pipe βBβ is opened 18 minutes after pipe βAβ, then find the total time taken to fill the tank in this manner.
Solution
Let the capacity of the tank be β150β litres {LCM (25, 30)} Efficiency of pipe βAβ = (150/25) = 6 litres/minute Efficiency of pipe βBβ = (150/30) = 5 litres/minute Quantity of water filled by pipe βAβ in 18 minutes = 18 Γ 6 = 108 litres Quantity of water to be filled = 150 β 108 = 42 litres Time taken by pipe βAβ and βBβ together to fill 42 litres of water = {42/(6 β 1)} = 42 minutes Total time taken = 18 + 42 = 60 minutes
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