Explanation:

To solve the problem, follow these steps:

- The initial investment ratios: A:B = 5:6, B:C = 3:7.

- Combine A:B and B:C to find A:B:C.

* A:B = 5:6

* B:C = 3:7.

* Equate B's part: Multiply A:B by 3 ? 15:18, and B:C by 6 ? 18:42.

* Therefore, A:B:C = 15:18:42.

- Adjust for the duration of investment:

* A's investment = 15 * 12 = 180

* B's investment = 18 * 10 = 180

* C's investment = 42 * 10 = 420

- Combine these to find the profit ratio: 180:180:420 or 1:1:2.33 approximately.

- Given A's share of profit = Rs. 1740.

- Calculate the total profit ratio: 1+1+2.33 = 4.33.

- Each part's value = 1740 / 1 (as A has a ratio of 1) = Rs. 1740.

- Thus, C's share = 2.33 * 1740 = Rs. 4055.82. Round off to Rs. 4060.

- Correct Answer: Option:1, Rs. 4060