Question
Pipes X and Y can fill a water tank individually in 24
minutes and 36 minutes, respectively. A third pipe Z can empty the tank in 72 minutes. If all three pipes are opened at the same time, how long (in seconds) will it take to fill the tank?Solution
ATQ,
Let the capacity of the tank be 72 litres (LCM of 24, 36, and 72)
Efficiency of X = 72 ÷ 24 = 3 litres/minute
Efficiency of Y = 72 ÷ 36 = 2 litres/minute
Efficiency of Z = 72 ÷ 72 = 1 litre/minute (outlet)
Required time = 72 ÷ (3 + 2 - 1) = 72 ÷ 4 = 18 minutes = 18 × 60 = 1,080 seconds
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