Amar, Bhavan and Chetan started a business with investments of Rs.8000, Rs.16000 and Rs.12000 respectively. After x months, Bhavan and Chetan left the business simultaneously. At the end of the year, the profit shares of Bhavan, Amar and Chetan are in descending order and x is an integer, find x.
Question
Amar, Bhavan and Chetan started a business with investments of Rs.8000, Rs.16000 and Rs.12000 respectively. After x months, Bhavan and Chetan left the business simultaneously. At the end of the year, the profit shares of Bhavan, Amar and Chetan are in descending order and x is an integer, find x.
Solution
The profit share of each person in a business partnership is directly proportional to the product of the initial investment and the time for which the investment was kept in the business.
Let's denote the profit shares of Amar, Bhavan, and Chetan as P(A), P(B), and P(C) respectively.
Given that Amar invested Rs.8000 for 12 months, Bhavan invested Rs.16000 for x months, and Chetan invested Rs.12000 for x months, we can write the following equations:
P(A) = 8000 * 12 = 96000 P(B) = 16000 * x P(C) = 12000 * x
We know that P(B) > P(A) > P(C), which means:
16000 * x > 96000 > 12000 * x
Solving these inequalities for x, we get:
x > 96000 / 16000 = 6 96000 / 12000 > x > 6
So, x must be greater than 6 but less than 8. Since x is an integer, the only value that satisfies these conditions is x = 7.
Therefore, Bhavan and Chetan left the business after 7 months.
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