X, Y and Z share profit and losses in the ratio of 5 : 3 : 2, Z retires and his share is taken by X and Y in the ratio of 1 : 2. The new profit-loss sharing ratio between X and Y will be:

The correct answer is $\boxed{\text{A}}$.

Let’s solve this problem step-by-step.

Initially, X, Y, and Z share profit and losses in the ratio of 5 : 3 : 2. This means that X’s share is 5 parts, Y’s share is 3 parts, and Z’s share is 2 parts.

If Z retires and his share is taken by X and Y in the ratio of 1 : 2, then X will get 1/3 of Z’s share and Y will get 2/3 of Z’s share.

The new profit-loss sharing ratio between X and Y will be 5 + 1/3 : 3 + 2/3 = 16/3 : 11/3 = 17 : 13.

Therefore, the correct answer is $\boxed{\text{A}}$.

Here is a brief explanation of each option:

• Option A: 17 : 13. This is the correct answer.
• Option B: 11 : 7. This is not the correct answer because it does not take into account the fact that Z’s share is taken by X and Y in the ratio of 1 : 2.
• Option C: 10 : 7. This is not the correct answer because it does not take into account the fact that Z’s share is taken by X and Y in the ratio of 1 : 2.
• Option D: 6 : 5. This is not the correct answer because it does not take into account the fact that Z’s share is taken by X and Y in the ratio of 1 : 2.