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      Question

      X takes twice as much time as Y or thrice as much time

      as Z to finish a job. Working together, the trio can finish the job in 2 days. Y alone can do the work in __________.
      A 6 days Correct Answer Incorrect Answer
      B 6 days Correct Answer Incorrect Answer
      C 8 days Correct Answer Incorrect Answer
      D 15 days Correct Answer Incorrect Answer

      Solution

      Let Y = y days Then X = 2y days Also, X = 3z ⇒ z = (2/3)y Rates: X = 1/(2y) Y = 1/y Z = 1/z = 1/((2/3)y) = 3/(2y) Together: 1/(2y) + 1/y + 3/(2y) = 1/2 (1 + 2 + 3)/(2y) = 1/2 6/(2y) = 1/2 3/y = 1/2 y = 6

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