A started a business by investing Rs.1200. After some months, B joined with an investment of Rs.3600. Two months later, C joined the business by investing Rs.2800. If the annual profit shares of A and B are equal, find the number of months C invested his money.

Question

Accepted Answer

**Solution:**

1. Let the total duration of the business be 12 months.

2. Suppose A invested for the entire 12 months.

3. Let B joined after *x* months, so B invested for (12 - x) months.

4. C joined 2 months after B, so C invested for (12 - x - 2) months.

5. Given investments:
   - A = Rs.1200
   - B = Rs.3600
   - C = Rs.2800

6. The profit share is proportional to the product of investment and time invested.

7. Since A and B have equal profit shares:
   $$1200 	imes 12 = 3600 	imes (12 - x)$$

8. Simplify:
   $$14400 = 3600 	imes (12 - x)$$
   $$12 - x = \frac{14400}{3600} = 4$$
   $$x = 12 - 4 = 8$$

9. Therefore, B joined after 8 months.

10. C joined 2 months after B, so C invested for:
    $$12 - 8 - 2 = 2 	ext{ months}$$

**Answer:** 2 months

Answer

Answer

Answer

Answer