New profit →
Let the total profits of firm = 1.
Z ' s share of profits = 3 /7 .
Remaining share of profit = 1 – 3 /7 = 4 /7.

:: It is shared by X & Y in their old profit Ratio i.e., 3 : 2.'
✓ X 's new share = 3 /5 of 4 /7 = 12 / 35 .
✓Y ' s new share = 2/5 of 4 /7 = 8 / 35.
✓Z 's new share ( given ) 3 / 7 or 15 /35.
✓Thus , new profit sharing Ratio of X, Y & Z will be 12 : 8 : 15.
Sacrifice Ratio → old ratio – new ratio .↓
: X ' sacrifice = 3 /5 – 12 / 35 = 9 /35.
Y 's Sacrifice = 2 /5 – 8 / 35 = 6 /35.
so , the sacrifice Ratio of X & Y = 9 : 6 or 3 : 2.

Introduction:
In a partnership firm, the profit sharing ratio determines how the profits and losses will be divided among the partners. When a new partner joins the firm, the existing partners may need to adjust their profit sharing ratios to accommodate the new partner's share. This adjustment is known as the new profit sharing ratio. Additionally, the partners who have to give up a portion of their share are said to have sacrificed their share, and this is known as the sacrificing ratio.

Given Information:
- X and Y are partners in a firm sharing profit and losses in the ratio of 3:2.
- Z is a new partner who will receive a 3/7 share in the profit.

Calculation of New Profit Sharing Ratio:
To calculate the new profit sharing ratio, we need to consider the share of each partner in the total profit.

The initial profit sharing ratio between X and Y is 3:2, which can be represented as 3x and 2x, where x is a constant.

As Z is entitled to a 3/7 share in the profit, we can represent Z's share as (3/7)y, where y is a constant.

Now, the new profit sharing ratio can be calculated by adding the shares of X, Y, and Z.

New Profit Sharing Ratio = (3x + 2x + (3/7)y) : (2x + 3x + (4/7)y)
= (5x + (3/7)y) : (5x + (4/7)y)

Calculation of Sacrificing Ratio:
The sacrificing ratio is determined by comparing the existing profit sharing ratio with the new profit sharing ratio.

Sacrificing Ratio = Old Ratio - New Ratio

Old Ratio = 3:2
New Ratio = (5x + (3/7)y) : (5x + (4/7)y)

Sacrificing Ratio = (3:2) - ((5x + (3/7)y) : (5x + (4/7)y))

Conclusion:
The new profit sharing ratio is (5x + (3/7)y) : (5x + (4/7)y) and the sacrificing ratio can be calculated by subtracting the new ratio from the old ratio. These calculations help determine the revised distribution of profits among the partners in the firm.