Select the correct answerA,B and C started a business with their capitals in the ratio 2:3:5. A increased his capital by 50% after 4 months, B increased his capital by 3313% after 6 months and C withdrew 50% of his capital after 8 months, from the start of the business. If the total profit at the end of a year was Rs 86,800, then the difference between the shares of A and C in the profit was?OptionsRs 7,000Rs 12,600Rs 8,400

To solve this problem, we first need to understand that the share of profit in a business is directly proportional to the product of the capital invested and the time for which it is invested.

1. Let's assume the initial capitals of A, B and C as 2x, 3x and 5x respectively.

2. A increased his capital by 50% after 4 months. So, for the first 4 months, his capital was 2x and for the next 8 months, it was 2x * 150/100 = 3x. Therefore, A's capital-time contribution = 2x4 + 3x8 = 32x.

3. B increased his capital by 3313% after 6 months. So, for the first 6 months, his capital was 3x and for the next 6 months, it was 3x * 3413/100 = 102.39x. Therefore, B's capital-time contribution = 3x6 + 102.39x6 = 633.36x.

4. C withdrew 50% of his capital after 8 months. So, for the first 8 months, his capital was 5x and for the next 4 months, it was 5x * 50/100 = 2.5x. Therefore, C's capital-time contribution = 5x8 + 2.5x4 = 48x.

5. The total capital-time contribution = 32x + 633.36x + 48x = 713.36x.

6. Let's say the share of A, B and C in the profit are Sa, Sb and Sc respectively. Then, Sa/Sb/Sc = 32x/633.36x/48x = 32/633.36/48.

7. The total profit at the end of the year was Rs 86,800. So, Sa + Sb + Sc = 86,800.

8. From point 6 and 7, we can calculate the individual shares of A, B and C in the profit.

9. The difference between the shares of A and C in the profit = |Sa - Sc|.

Without the actual numerical values, we cannot determine the exact difference between the shares of A and C in the profit. However, we can see that B's capital-time contribution is significantly higher than A's and C's, so B will have the largest share of the profit. Between A and C, C's capital-time contribution is higher, so C will have a larger share than A. Therefore, the difference between the shares of A and C in the profit will be a positive number.