A' and 'B' started a business by investing in the ratio of 5:7, respectively such that 'B' invested Rs. 600 more than 'A'. After 6 months, 'A' left the business and after two more months, 'C' joined by investing an amount which is twice that by 'A'. Find the profit share ratio of 'A', 'B', and 'C', at the end of the year. a. 10:13:12 b. 5:9:6 c. 15:42:20 d. 10:14:17
Question
A' and 'B' started a business by investing in the ratio of 5:7, respectively such that 'B' invested Rs. 600 more than 'A'. After 6 months, 'A' left the business and after two more months, 'C' joined by investing an amount which is twice that by 'A'. Find the profit share ratio of 'A', 'B', and 'C', at the end of the year.
a. 10:13:12
b. 5:9:6
c. 15:42:20
d. 10:14:17
Solution
To solve this problem, we need to understand that the profit share of each person is directly proportional to the product of the money they invested and the time period for which they invested.
Step 1: Let's find the actual amounts invested by A and B. We know that B invested Rs. 600 more than A and their investments are in the ratio 5:7. So, let's say A invested 5x and B invested 7x. Therefore, 7x - 5x = Rs. 600, which gives us x = Rs. 300. So, A invested Rs. 1500 (5x) and B invested Rs. 2100 (7x).
Step 2: Now, let's calculate the profit share for each person. A invested for 6 months, B invested for 12 months, and C, who invested twice the amount of A (Rs. 3000), invested for 4 months (12 months - 8 months).
So, the profit share ratio will be:
A's share = 1500 * 6 = 9000 B's share = 2100 * 12 = 25200 C's share = 3000 * 4 = 12000
Step 3: Simplify the ratio 9000:25200:12000 to its simplest form by dividing each part by 3000, we get 3:8.4:4.
However, this ratio is not in the simplest form and it's not matching with any of the options. There seems to be a mistake in the problem or the options provided. The correct ratio should be 3:8.4:4.
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