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    Question

    A and B started a business with investments of Rs.

    12,800 and Rs. 16,000, respectively. After a few months, C joined them with an investment of Rs. 9,600. At the end of 16 months, the total profit of Rs. 5,400 was distributed, and C received a share of Rs. 1,080. Based on this, determine after how many months C joined the business.
    A 6 months Correct Answer Incorrect Answer
    B 3 months Correct Answer Incorrect Answer
    C 4 months Correct Answer Incorrect Answer
    D 9 months Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let the time for which 'C' invest in the business be 'n' months. Ratio of profit shares of 'A', 'B' and 'C' respectively: = (12,800 X 16) :(16,000 X 16) :(9,600 X n) = 64:80:3n So, 3n ÷ (64 + 80 + 3n) = (1,080/5,400) Or, 3n ÷ (144 + 3n) = (1/5) Or, 15n = 144 + 3n Or, 12n = 144 Or, 'n' = 12 Therefore, time after which 'C' joined the business = 16 - 12 = 4 months

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