A started a business with an initial investment. After 3 months, B joined with Rs. 20,000. After another 4 months, C joined with Rs. 25,000. The ratio of the profit shares of A and B is 8:3. If the total profit at the end is Rs. 15,700, what is A's share of the profit?

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**Solution:**

1. Let A's initial investment be Rs. *x*.

2. B joins after 3 months with Rs. 20,000, so B's investment duration is (12 - 3) = 9 months.

3. C joins after 7 months (3 + 4 months) with Rs. 25,000, so C's investment duration is (12 - 7) = 5 months.

4. The profit share is proportional to the product of investment and time period.

5. Given the ratio of profit shares of A and B is 8:3, so:
   $$ \frac{A 	imes 12}{20,000 	imes 9} = \frac{8}{3} $$

6. Simplify to find A's investment:
   $$ \frac{12x}{180,000} = \frac{8}{3} \implies \frac{x}{15,000} = \frac{8}{3} \implies x = 15,000 	imes \frac{8}{3} = 40,000 $$

7. Now calculate the investment-time products:
   - A: $40,000 	imes 12 = 480,000$
   - B: $20,000 	imes 9 = 180,000$
   - C: $25,000 	imes 5 = 125,000$

8. Total investment-time product = $480,000 + 180,000 + 125,000 = 785,000$

9. A's share of profit =
   $$ \frac{480,000}{785,000} 	imes 15,700 = \frac{480}{785} 	imes 15,700 $$

10. Calculate:
    $$ \approx 0.6115 	imes 15,700 = 9,600 $$

**Answer:** Rs. 9600

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