Question
Pipes P and Q alone can fill a tank in 6 hours and 3
hours respectively. When both pipes along with pipe R, an outlet pipe, are opened together, 2/5 of the tank gets filled in 60 minutes. Find the time taken by pipe R to empty a completely filled tank.Solution
Let the total capacity of the tank be 30 litres.
Efficiency of Pipe 'P' = 30 / 6 = 5 litres/hour
Efficiency of Pipe 'Q' = 30 / 3 = 10 litres/hour
Let pipe 'R' empties the tank with an efficiency of 'm' litres/hour.
Tank filled in 60 minutes = (2/5) × 30 = 12 litres
ATQ,
(5 + 10 - m) × (60/60) = 12
(15 - m) × 1 = 12
15 - m = 12
m = 3 litres/hour
Time taken by R to empty the tank = 30 / 3 = 10 hours
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