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    Ram started a business with an investment of ₹ 70,000 . After a few months, Sham joined him with ₹ 60,000 . At the end of the year, the profits were i
    Question

    Ram started a business with an investment of ₹ 70,000 . After a few months, Sham joined him with ₹ 60,000 . At the end of the year, the profits were in the ratio of 2:1. After how many months did Sham join ?

    A.

    5 months

    B.

    3 months

    C.

    4 months

    D.

    6 months

    Correct option is A

    Given:
    Ram's investment = ₹70000 for 12 months
    Sham's investment = ₹60000 for t months
    Profit ratio = 2:1
    Formula Used:
    Ratio of Profits = Ratio of (Investment × Time)
    Solution:
    Let Sham's investment period be t months.
    Profit Ratio = Rams Investment×Rams TimeShams Investment×Shams Time \frac{Ram's\ Investment × Ram's\ Time}{Sham's\ Investment × Sham's\ Time}​​
    70000×1260000×t=21\frac{70000 × 12}{60000 × t} = \frac{2}{1}​​

    7×126×t=2\frac{7 × 12}{6 × t} = 2​​

    846t=2\frac{84}{6t} = 2​​

    14t=2\frac{14}{t} = 2​​
    t = 7 months
    Sham invested his money for 7 months.
    Therefore, he joined after (12 - 7) = 5 months.
    Final Answer
    So the correct answer is (a)

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