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      Question

      Pipe ‘A’ and pipe ‘B’ can fill a tank alone in

      45 hours and 15 hours, respectively. If both pipes are opened together and pipe ‘B’ is closed after 6 hours, then find the time taken by pipe ‘A’ to fill the remaining portion of the tank alone.
      A 18 hours Correct Answer Incorrect Answer
      B 30 hours Correct Answer Incorrect Answer
      C 24 hours Correct Answer Incorrect Answer
      D 21 hours Correct Answer Incorrect Answer

      Solution

      Let the capacity of the tank be 45 units (LCM of 45 and 15) Efficiency of pipe ‘A’ = 45 ÷ 45 = 1 unit/hour
      Efficiency of pipe ‘B’ = 45 ÷ 15 = 3 unit/hour Let pipe ‘A’ fill the remaining portion in x hours. ATQ, 6 × (1 + 3) + 1x = 45 Or, 24 + x = 45 Or, x = 21 Therefore, required time taken = 21 hours

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