Question
Time taken by ‘A’ to fill a tank, which is 60%
empty, is 24 minutes, while time taken by ‘B’ to fill the same tank, when it is 40% full, is 30 minutes. When the tank is completely empty, both pipes are opened together. Find the time after which ‘A’ must be closed so that the tank gets filled in 28 minutes.Solution
Time taken by ‘A’ to fill the empty tank = {24/0.6} = 40 minutes Time taken by ‘B’ to fill the empty tank = {30/0.6} = 50 minutes Let the total capacity of the tank be 200 litres Efficiency of ‘A’ = {200/40} = 5 litres/minute Efficiency of ‘B’ = {200/50} = 4 litres/minute Let the time after which ‘A’ is closed be T minutes. ATQ, (5 + 4)T + 4(28 - T) = 200 9T + 112 - 4T = 200 5T = 88 T = 17.6 or 17 minutes 36 seconds
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