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    Question

    ‘P’ began a business by investing Rs. 24000. After (x +

    2) months, ‘Q’ entered with Rs. 18000, and again after (x + 2) more months, ‘R’ joined them by investing Rs. 30000. If the profit-sharing ratio among them at the end of the year was 8:6:5 respectively, then after how many months from the beginning did ‘R’ join?
    A 12 months Correct Answer Incorrect Answer
    B 5 months Correct Answer Incorrect Answer
    C 2 months Correct Answer Incorrect Answer
    D 10 months Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ,

    Profit sharing ratio of P, Q and R respectively

    = (24000 × 12) : {18000 × (12 – x – 2)} : {30000 × (12 – x – 2 – x – 2)}

    = 96 : {3(10 – x)} : {5(8 – 2x)}

    According to the question,

    96 / {3(10 – x)} = 8 / 6

    ⇒ 10 – x = 6

    ⇒ x = 4

    Required time after which R joined the business = (x + 2 + x + 2) = (2x + 4) = 12 months

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