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      Question

      Find the relation between the given below

      quantities: Quantity I: A can complete a work in x - 4 days and B can complete the same work in x + 4 days. The same work is completed when A works for 6 days and B works for 10 days. In how many days can both A and B together complete the work? Quantity II: A can complete a work in x + 2 days and B can complete the same work in x - 2 days. The same work is completed when A completes 75% of the work and B does the rest in total 23 days. In how many days can both A and B together complete the work when A works with 20% higher efficiency?
      A Quantity I > Quantity II Correct Answer Incorrect Answer
      B Quantity I < Quantity II Correct Answer Incorrect Answer
      C Quantity I ≤ Quantity II Correct Answer Incorrect Answer
      D Quantity I ≥ Quantity II Correct Answer Incorrect Answer
      E Quantity I = Quantity II Correct Answer Incorrect Answer

      Solution

      ATQ, Quantity I A’s efficiency = 1/(x - 4) B’s efficiency = 1/(x + 4) 6/(x - 4) + 10/(x + 4) = 1 6(x + 4) + 10(x - 4) = (x - 4)(x + 4) 6x + 24 + 10x - 40 = x² - 16 16x - 16 = x² - 16 x² - 16x = 0 x(x - 16) = 0 So, x = 16 A = 12 days B = 20 days LCM = 60 A’s part = 5 B’s part = 3 Together time = 60/8 = 7.5 days Quantity II A’s efficiency = 1/(x + 2) B’s efficiency = 1/(x - 2) 3/4(x + 2) + 1/4(x - 2) = 23 3x + 6 + x - 2 = 92 4x + 4 = 92 4x = 88 x = 22 A = 24 days B = 20 days A works with 20% higher efficiency New A’s time = 24 × 5/6 = 20 days Now both times = 20 days and 20 days Together time = 20/2 = 10 days Final Comparison: Quantity I = 7.5 days Quantity II = 10 days Quantity I < Quantity II Correct option: B

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