Question
Pipe 'A' and pipe 'B', alone can fill a tank in 20 minutes and 30 minutes, respectively. Both the pipes were opened together to fill the tank, but later it was found that it took 3 minutes extra to fill the tank due to a leak. Find the time taken by the leak to empty the tank when it is completely full.
Solution
Let total capacity of the tank be 60 units {LCM of 20, 30} Therefore, efficiency of pipe 'A' = (60/20) = 3 units/minutes Therefore, efficiency of pipe 'B' = (60/30) = 2 unit/minutes Sum of efficiency of both the pipes = 5 units/minutes Time taken by pipes 'A' and 'B' together to fill the tank = (60/5) = 12 minutes But due the leakage actual time taken by pipes 'A' and 'B' together to fill the tank = (12 + 3) = 15 minutes Therefore, effective efficiency of the pipes and the leak = (60/15) = 4 units/minutes Efficiency of the leak = (5 - 4) = 1 unit/minute Required time = (60/1) = 60 minutes
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