Question
Pipe X can fill a tank on its own
in 12 hours, while Pipe Y can fill the same tank individually in 20 hours. Both pipes X and Y operate together for 4 hours, after which Pipe P is introduced. Pipe P, when working alone, can drain the fully filled tank in 15 hours. Determine the total time required to fill the tank under these conditions.Solution
ATQ,
Let the capacity of the tank be 60 litres. {LCM (12, 20 and 15)} Efficiency of pipe 'X' = (60/12) = 5 litres/hour Efficiency of pipe 'Y' = (60/20) = 3 litres/hour Efficiency of outlet pipe 'Z' = (60/15) = 4 litres/hour Quantity of water filled by pipe 'X' and 'Y' together in 4 hours = (5 + 3) × 4 = 32 litres Combined efficiency of all three pipes = 5 + 3 - 4 = 4 litres/hour So, time taken to fill the remaining tank = {(60 - 32)/4} = 7 hours So, total time taken = 7 + 4 = 11 hours
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