New Profit-Sharing Ratio and Sacrificing Ratio Calculation

New Profit-Sharing Ratio Calculation:
1. Existing ratio of profit sharing between A and B is 3:1
2. The profit-sharing ratio between B and C shall be the same as existing between A and B
3. Let X be the profit-sharing ratio between B and C
4. Then, we can write the equation as:
3:1 = 1:X
5. Solving for X, we get X = 1/3
6. Hence, the new profit-sharing ratio between A, B, and C is 3:1:1/3 or 9:3:1

Sacrificing Ratio Calculation:
1. Sacrificing ratio is the ratio in which the existing partners give up their share in favor of the new partner
2. Let D be the new partner who is being admitted into the firm
3. The sacrificing ratio of A and B is the ratio in which they give up their share in favor of D
4. Let Y be the sacrificing ratio of A and B
5. Then, we can write the equation as:
3:1 = (9-Y):Y
6. Solving for Y, we get Y = 2/11
7. Hence, the sacrificing ratio of A and B is 2:9

Explanation of Admission of a New Partner

Admission of a new partner into an existing firm means that a new person is being added as an owner of the business. The new partner may bring in capital, expertise, or other resources that can help the firm grow and become more profitable. However, admitting a new partner also requires a revaluation of the assets and liabilities of the firm, as well as a renegotiation of the profit-sharing ratios between the existing partners.

The admission of a new partner involves the following steps:

1. Calculation of the new profit-sharing ratio between all partners, including the new partner
2. Calculation of the sacrificing ratio of the existing partners, which determines the extent to which they give up their share in favor of the new partner
3. Revaluation of the assets and liabilities of the firm to reflect the new partner's contribution
4. Adjustment of the capital accounts of all partners to reflect the new profit-sharing ratio and the revaluation of assets and liabilities.

The admission of a new partner can help a firm expand its operations, increase its profitability, and diversify its risks. However, it also requires careful planning and negotiation to ensure that all partners are satisfied with the new arrangements.

New Profit Sharing Ratio = 9:3:1
Sacrificing Ratio = 3:1