Explanation:

- A invests Rs. 5000 for 12 months. His total contribution is 5000 x 12 = 60000.

- B joins after 6 months, investing for 6 months.

- At year-end, A and B's total profit is Rs. 8700.

- B's share of the profit is Rs. 2700.

- The ratio of profits is determined by the investments multiplied by the time.

- Let's say B invests Rs. X. His contribution is X x 6.

- Profit ratio: \( \frac{5000 \times 12}{X \times 6} = \frac{60000}{6X} \)

- Given A's profit: 8700 - 2700 = 6000.

- Profit ratio \( \frac{6000}{2700} = \frac{60000}{6X} \).

- Solving gives X = Rs. 4500.

- Correct Answer: Option 4 - Rs. 4500