Question
Pipes X and Y can fill a tank in 48 minutes and 80 minutes
respectively. Another pipe Z can empty the tank in 2 hours. X and Z are opened together. If after 36 minutes, Y is also opened, then how long will it take to fill the tank completely?Solution
ATQ,
Let the capacity of the tank be 240 litres (LCM of 48, 80 and 120)
Efficiency of X = 240 ÷ 48 = 5 litres/minute
Efficiency of Y = 240 ÷ 80 = 3 litres/minute
Efficiency of Z = 240 ÷ 120 = -2 litres/minute (since it is an outlet pipe)
Tank filled in 36 minutes = (5 - 2) × 36 = 108 litres
Remaining tank to be filled = 240 - 108 = 132 litres
Time to fill remaining = 132 ÷ (5 + 3 - 2) = 132 ÷ 6 = 22 minutes
Total time taken = 36 + 22 = 58 minutes
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