The correct answer is $\boxed{\text{A. 1 : 2}}$.
The initial ratio of A and B is 5 : 3. This means that A has 5 parts and B has 3 parts. When C joins, the new ratio agreed is 4 : 2 : 2. This means that A now has 4 parts, B now has 2 parts, and C now has 2 parts.
To find the sacrificing ratio of A and B, we need to find the difference between their initial ratio and their new ratio. The initial ratio of A and B is 5 : 3, and their new ratio is 4 : 2. The difference between these two ratios is 1 : 1. This means that A is sacrificing 1 part and B is sacrificing 1 part.
Therefore, the sacrificing ratio of A and B is $\boxed{\text{1 : 2}}$.
Here is a more detailed explanation of each option:
- Option A: $\boxed{\text{1 : 2}}$. This is the correct answer. A is sacrificing 1 part and B is sacrificing 1 part, so the sacrificing ratio of A and B is 1 : 2.
- Option B: $\boxed{\text{1 : 3}}$. This is incorrect. A is sacrificing 1 part and B is sacrificing 1 part, so the sacrificing ratio of A and B is 1 : 2, not 1 : 3.
- Option C: $\boxed{\text{1 : 1}}$. This is incorrect. A is sacrificing 1 part and B is sacrificing 1 part, so the sacrificing ratio of A and B is 1 : 2, not 1 : 1.
- Option D: $\boxed{\text{None if the above}}$. This is incorrect. The correct answer is $\boxed{\text{1 : 2}}$.