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      Question

      Pipe ‘A’ can fill a tank in 40 hours whereas leak

      ‘A’ can empty it in 50 hours. If they both operate along with pipe ‘B’, then the given tank gets filled in 20 hours. How much time is needed to fill the given tank if pipe ‘B’ and leak ‘A’ work together?  
      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 200 litres {LCM (40 and 50)} Efficiency of pipe ‘A’ = 200 ÷ 40 = 5 litres/hour Efficiency of leak ‘A’ = 200 ÷ 50 = 4 litres/hour Combined efficiency of pipe ‘A’ and leak ‘A’ = 5 – 4 = 1 litre/hour Combined efficiency of pipe ‘A’, ‘B’ and leak ‘A’ = 200 ÷ 20 = 10 units/hour Efficiency of pipe ‘B’ = 10 – 1 = 9 units/hour Time taken by pipe ‘B’ and leak ‘A’ to fill the tank = 200 ÷ (9 – 4) = 40 hours

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