Explanation:

- A and B together complete the work in 10 days. So, their combined work rate is 1/10 of the work per day.

- B and C together complete the work in 12 days. Their combined work rate is 1/12 of the work per day.

- C and A together complete the work in 15 days. Their combined work rate is 1/15 of the work per day.

To find the individual work rate of A, B, and C, we sum the equations:

- (A + B) + (B + C) + (C + A) = 2(A + B + C)

This yields:

- 1/10 + 1/12 + 1/15 = 2(A + B + C)

After calculating, we find:

- A + B + C = 1/8

This means A, B, and C together can complete the whole work in 8 days. Therefore, they can finish half of the work in 4 days.

- Correct Option: Option 3 - 4 days