Question
Pipes P and Q can fill a tank in 90 minutes and 60 minutes respectively. Another pipe R can drain the tank in 2 hours 30 minutes. Q and R are opened together. After 40 minutes, Q is turned off and P is opened. How much total time will it take to fill the tank?
Solution
ATQ,
Let the capacity of tank be 180 litres (LCM of 90, 60 and 150) Efficiency of 'P' = 180 ÷ 90 = 2 litres/minute Efficiency of 'Q' = 180 ÷ 60 = 3 litres/minute Efficiency of 'R' (outlet pipe) = 180 ÷ 150 = -1.2 litres/minute Tank filled in 40 minutes = (3 - 1.2) × 40 = 72 litres Remaining tank = 180 - 72 = 108 litres Time taken to fill remaining = 108 ÷ (2 - 1.2) = 135 minutes Required total time = 40 + 135 = 175 minutes
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