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      Question

      A tank has three pipes, X, Y, and Z. X can fill the tank

      in 8 hours, Y can fill it in 12 hours, and Z can empty it in 6 hours. If X, Y, and Z are opened together, how long will it take to fill the tank?
      A 24 hours Correct Answer Incorrect Answer
      B 30 hours Correct Answer Incorrect Answer
      C 18 hours Correct Answer Incorrect Answer
      D 20 hours Correct Answer Incorrect Answer
      E 16 hours Correct Answer Incorrect Answer

      Solution

      Work done by X in 1 hour = 1/8 Work done by Y in 1 hour = 1/12 Work done by Z in 1 hour (emptying) = -1/6 Net work in 1 hour = (1/8) + (1/12) - (1/6) Taking LCM of 8, 12, and 6 = 24, Net work = (3/24) + (2/24) - (4/24) = 1/24 The tank will be filled in 24 hours.

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