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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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