Explanation:

- X and Y share profits in the ratio of 3:2, meaning if the total profit is divided into 5 equal parts, X gets 3 parts, and Y gets 2 parts.

- Z joins with a 1/4 share of total profits, acquiring this equally from both X and Y.

- Hence, X and Y together contribute a 1/4 share to Z.

- X loses half of Z's share, which is 1/8, so X's new share = 3/5 - 1/8 = 19/40.

- Y also loses half of Z's share, which is 1/8, so Y's new share = 2/5 - 1/8 = 11/40.

- Z receives a 1/4 share, which is 10/40.

- Therefore, the new profit sharing ratio among X, Y, and Z is 19:11:10.

Option: 2, 19:11:10