Question
Time taken by ‘A’ to fill a tank, which is 50%
empty, is 20 minutes, while time taken by ‘B’ to fill the same tank, when it is 25% full, is 30 minutes. On a particular day, when the tank is completely empty, ‘A’ and ‘B’ are opened together. Find the time (in minutes) after which ‘A’ must be closed so that the tank gets completely filled in 24 minutes.Solution
Time taken by ‘A’ to fill the empty tank = {20/0.5} = 40 minutes Time taken by ‘B’ to fill the empty tank = {30/0.75} = 40 minutes Let the total capacity of the tank be 400 litres Efficiency of ‘A’ = {400/40} = 10 litres/minute Efficiency of ‘B’ = {400/40} = 10 litres/minute Let the time after which ‘A’ is closed be T minutes. ATQ, (10 + 10)T + 10(24 - T) = 400 20T + 240 - 10T = 400 10T = 160 T = 16
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