Explanation:

- A's investment: Rs. 50,000 for 12 months.

- B's investment: Rs. 80,000 for 12 months.

- C joins later: After 4 months; hence, C is in business for 8 months.

- Profit sharing: Based on the investment and the period the investment is used.

Let's find out C's investment using the profit-sharing ratio:

- A's contribution = \( 50000 \times 12 = 600000 \)

- B's contribution = \( 80000 \times 12 = 960000 \)

- Let C's investment be Rs. X.

- C's contribution = \( X \times 8 \)

Total profit = Rs. 40,000.

C's share = Rs. 15,000. Hence,

$$ \frac{X \times 8}{600000 + 960000 + X \times 8} \times 40000 = 15000 $$

Solve for X:

$$ \frac{8X}{1560000 + 8X} = \frac{15}{40} $$

$$ 32X = 2340000 + 12X $$

$$ 20X = 2340000 $$

$$ X = \frac{2340000}{20} = 117000 $$

- Correct answer: Option 3: Rs. 117,000