X and Y are partners, sharing profits and losses in the ratio of 4:3. They admit Z into the partnership…

The old profit-sharing ratio of X and Y is 4:3 (4/7 and 3/7). After admitting Z for a 1/5 share, the remaining 4/5 share is divided between X and Y in their new ratio of 2:1, giving X a new share of (2/3)*(4/5) = 8/15 and Y a new share of (1/3)*(4/5) = 4/15. Subtracting new shares from old shares gives X's sacrifice = 4/7 - 8/15 = 4/105 and Y's sacrifice = 3/7 - 4/15 = 17/105, yielding a sacrificing ratio of 4:17.