Three persons start a business with capitals in the ratio \frac{1}{3}:\frac{1}{4}:\frac{1}{5}. The first person withdraws half his capital after 4 months. What is his share of profit if the business fetches an annual profit of 96,800?

Explanation

Initial capital ratio is \frac{1}{3}:\frac{1}{4}:\frac{1}{5} = 20:15:12. The effective capital of the first person is (20 \times 4) + (10 \times 8) = 160. For the second and third persons, it is 15 \times 12 = 180 and 12 \times 12 = 144 respectively. Profit sharing ratio = 160:180:144 = 40:45:36. The first person's share = \frac{40}{121} \times 96800 = 32,000.

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