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      Question

      Pipe β€˜A’ can fill a tank in 50 hours whereas leak

      β€˜A’ can empty it in 60 hours. If they both operate along with pipe β€˜B’, then the given tank gets filled in 30 hours. How much time is needed to fill the given tank if pipe β€˜B’ and leak β€˜A’ work together?Β Β 
      A 40 hours Correct Answer Incorrect Answer
      B 60 hours Correct Answer Incorrect Answer
      C 75 hours Correct Answer Incorrect Answer
      D 30 hours Correct Answer Incorrect Answer
      E 84 hours Correct Answer Incorrect Answer

      Solution

      Let the capacity of the tank be 300 litres {LCM (50 and 60)} Efficiency of pipe β€˜A’ = 300 Γ· 50 = 6 litres/hour Efficiency of leak β€˜A’ = 300 Γ· 60 = 5 litres/hour Combined efficiency of pipe β€˜A’ and leak β€˜A’ = 6 – 5 = 1 litre/hour Combined efficiency of pipe β€˜A’, β€˜B’ and leak β€˜A’ = 300 Γ· 30 = 10 units/hour Efficiency of pipe β€˜B’ = 10 – 1 = 9 units/hour Time taken by pipe β€˜B’ and leak β€˜A’ to fill the tank = 300 Γ· (9 – 5) = 75 hours

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