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.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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