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      Question

      Pipe β€˜A’ can fill a tank in 60 hours whereas leak

      β€˜A’ can empty it in 70 hours. If they both operate along with pipe β€˜B’, then the given tank gets filled in 35 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 420 litres {LCM (60 and 70)} Efficiency of pipe β€˜A’ = 420 Γ· 60 = 7 litres/hour Efficiency of leak β€˜A’ = 420 Γ· 70 = 6 litres/hour Combined efficiency of pipe β€˜A’ and leak β€˜A’ = 7 – 6 = 1 litre/hour Combined efficiency of pipe β€˜A’, β€˜B’ and leak β€˜A’ = 420 Γ· 35 = 12 units/hour Efficiency of pipe β€˜B’ = 12 – 1 = 11 units/hour Time taken by pipe β€˜B’ and leak β€˜A’ to fill the tank = 420 Γ· (11 – 6) = 84 hours

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