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      Question

      The following questions each present two quantities,

      Quantity I and Quantity II. Compare the values of the two quantities and determine their relationship. X works at twice the efficiency of Y, and Z works at three times the efficiency of X. All three working together can finish a job in 12 days. Quantity I: X works alone for the first 14 days and then leaves. After that, Y and Z continue the remaining work on alternate days, with Y taking the first turn. How many total days will it take to finish the entire work? Quantity II: If each of them works alone to complete the entire work, what is the average number of days taken by X, Y, and Z?
      A Quantity > Quantity II Correct Answer Incorrect Answer
      B Quantity < Quantity II Correct Answer Incorrect Answer
      C Quantity I = Quantity II or No relation can be established Correct Answer Incorrect Answer
      D Quantity I ≥ Quantity II Correct Answer Incorrect Answer
      E Quantity I ≤ Quantity II Correct Answer Incorrect Answer

      Solution

      ATQ, Efficiency of X = 2x Efficiency of Y = x Efficiency of Z = 6x Total work = 9x×12 = 108x Quantity I: In 14 days X has done the work = (14×2) = 28x Remaining work = 108-28 = 80x In 2 days Y and Z will do = 7x units In 22 days then will do =77x units On the next day, Y will do = x unit of work Remaining work = 2x units Z will do the 2x unit work in = 2/6 = 1/3 days Total days taken to complete the work = 14+23 (1/3) days = 37 (1/3) days Quantity II: Time taken by Z alone to complete the whole work = 108x/6x = 18 days Time taken by X alone to complete the whole work = 108x/2x = 54 days Time taken by Y alone to complete the whole work = 108x/x = 108 days Required average = 18+54+108/3 = 60 days

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