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      Question

      Inlet pipes 'A' and 'B' can fill a tank in 24 minutes

      and 40 minutes, respectively. Both the pipes are opened together to fill the tank. When the tank is filled up to half of its capacity, a leak develops through which (1/4)th of the water supplied by both pipes goes out. Find the total time (in minutes) taken to fill the tank now.
      A 18.5 Correct Answer Incorrect Answer
      B 19 Correct Answer Incorrect Answer
      C 17.5 Correct Answer Incorrect Answer
      D 16.5 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Let the capacity of the tank be 120 litres (LCM of 24 and 40)
      Efficiency of 'A' = 120 ÷ 24 = 5 litres/minute
      Efficiency of 'B' = 120 ÷ 40 = 3 litres/minute
      Time to fill half tank = (0.5 × 120) ÷ (5 + 3) = 60 ÷ 8 = 7.5 minutes
      Effective rate after leak = (3/4) × (5 + 3) = 6 litres/minute
      Time to fill remaining = (0.5 × 120) ÷ 6 = 60 ÷ 6 = 10 minutes

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