Question
Pipes K and L alone can fill a tank in 4 hours and 6 hours
respectively. When both pipes along with pipe M, an outlet pipe, are opened together, 3/4 of the tank gets filled in 120 minutes. Find the time taken by pipe M to empty a completely filled tank.Solution
Let the total capacity of the tank be 12 litres.
Efficiency of Pipe 'K' = 12 / 4 = 3 litres/hour
Efficiency of Pipe 'L' = 12 / 6 = 2 litres/hour
Let pipe 'M' empties the tank with an efficiency of 'm' litres/hour.
Tank filled in 120 minutes = (3/4) × 12 = 9 litres
ATQ,
(3 + 2 - m) × (120/60) = 9
(5 - m) × 2 = 9
10 - 2m = 9
2m = 1
m = 0.5 litres/hour
Time taken by M to empty the tank = 12 / 0.5 = 24 hours
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