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      Question

      A set of Q men can complete a work in 20 days, while

      (Q+4) women can complete the same work in 28 days. If 9 men and 13 women together can finish the same work in 7 days, find Q.
      A 5 Correct Answer Incorrect Answer
      B 8 Correct Answer Incorrect Answer
      C 1 Correct Answer Incorrect Answer
      D 2 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

      Qm × 20 = (Q+4)w × 28

      5Qm = 7(Q+4)w

      m/w = (7Q+28) / 5Q

      Now,Q × (7Q+28) × 20 = [9 × (7Q+28) + 13 × 5Q] × 7

      140Q² + 560Q = 63Q + 252 + 65Q

      140Q² - 128Q - 252 = 0

      70Q² - 64Q - 126 = 0

      70Q² - 70Q + 6Q - 126 = 0

      10Q(7Q - 7) + 6(7Q - 7) = 0

      (7Q - 7)(10Q + 6) = 0

      Q = 7/7, -6/10

      Q = 1

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