Understanding New Profit-Sharing Ratio in Partnership Accounting

When a new partner is admitted into a partnership, the existing profit-sharing ratio among the old partners changes. The new partner brings in capital and gets a share in the future profits of the firm. This share is typically acquired from the old partners, who sacrifice a portion of their share. Calculating the new profit-sharing ratio is a fundamental step in partnership accounting upon the admission of a new partner.

Analyzing the Given Partnership Information

We are given information about a partnership firm with two existing partners, Anshu and Nitu, and the admission of a new partner, Jyoti. The key details provided are:

• Old partners: Anshu and Nitu.
• Old profit-sharing ratio of Anshu and Nitu: 3 : 2.
• New partner: Jyoti.
• Jyoti's share in the firm's future profits: 3/10th.
• How Jyoti acquires her share: 2/10th from Anshu and 1/10th from Nitu.

Based on the old ratio 3:2, Anshu's old share is $3/(3+2) = 3/5$ and Nitu's old share is $2/(3+2) = 2/5$.

Step-by-Step Calculation of New Profit-Sharing Ratio

To find the new profit-sharing ratio, we need to determine the new share of each partner after Jyoti's admission.

Calculating Old Partners' Sacrifice

The problem clearly states the share each old partner surrenders for the new partner.

• Anshu surrenders: 2/10th of the total profit.
• Nitu surrenders: 1/10th of the total profit.

The total share surrendered by Anshu and Nitu is \( \frac{2}{10} + \frac{1}{10} = \frac{3}{10} \), which matches Jyoti's share. This confirms the calculation method.

Calculating New Shares of Anshu and Nitu

Each old partner's new share is calculated by subtracting the share they surrendered from their original share. Anshu's New Share: Anshu's Old Share \( = \frac{3}{5} \) Share surrendered by Anshu \( = \frac{2}{10} \) Anshu's New Share \( = \) Anshu's Old Share \( - \) Share surrendered by Anshu Anshu's New Share \( = \frac{3}{5} - \frac{2}{10} \) To subtract these fractions, we need a common denominator, which is 10. \( \frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10} \) Anshu's New Share \( = \frac{6}{10} - \frac{2}{10} = \frac{6 - 2}{10} = \frac{4}{10} \) Nitu's New Share: Nitu's Old Share \( = \frac{2}{5} \) Share surrendered by Nitu \( = \frac{1}{10} \) Nitu's New Share \( = \) Nitu's Old Share \( - \) Share surrendered by Nitu Nitu's New Share \( = \frac{2}{5} - \frac{1}{10} \) To subtract these fractions, we need a common denominator, which is 10. \( \frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10} \) Nitu's New Share \( = \frac{4}{10} - \frac{1}{10} = \frac{4 - 1}{10} = \frac{3}{10} \)

Jyoti's Share

Jyoti's share in the new firm is given as \( \frac{3}{10} \).

Determining the New Profit-Sharing Ratio

The new profit-sharing ratio is the ratio of the new shares of all partners: Anshu, Nitu, and Jyoti. Anshu's New Share : Nitu's New Share : Jyoti's New Share \( \frac{4}{10} : \frac{3}{10} : \frac{3}{10} \) Since the denominators are the same (10), the ratio is simply the ratio of the numerators. New Profit-Sharing Ratio = 4 : 3 : 3.

Conclusion: New Profit-Sharing Ratio Calculation

The new profit-sharing ratio of Anshu, Nitu, and Jyoti is calculated as 4 : 3 : 3.

Partner	Old Share	Share Sacrificed	New Share
Anshu	\( \frac{3}{5} \) or \( \frac{6}{10} \)	\( \frac{2}{10} \)	\( \frac{4}{10} \)
Nitu	\( \frac{2}{5} \) or \( \frac{4}{10} \)	\( \frac{1}{10} \)	\( \frac{3}{10} \)
Jyoti	-	-	\( \frac{3}{10} \)

Revision Table: Partnership Ratios Summary

This table summarizes the different shares involved in the calculation.

Additional Information: Accounting Aspects of Partner Admission

Admitting a new partner involves several accounting adjustments beyond just calculating the new profit-sharing ratio. These may include:

• Sacrificing Ratio: This is the ratio in which the old partners agree to sacrifice their share of profits in favour of the new partner. In this question, Anshu sacrifices \( \frac{2}{10} \) and Nitu sacrifices \( \frac{1}{10} \). The sacrificing ratio is \( \frac{2}{10} : \frac{1}{10} \), or 2 : 1. This ratio is often used to distribute goodwill brought in by the new partner among the sacrificing partners.
• Goodwill: The new partner may be required to bring in a share of goodwill, representing the value of the firm's reputation. This goodwill is often adjusted through the partners' capital accounts based on the sacrificing ratio.
• Revaluation of Assets and Liabilities: Assets and liabilities are typically revalued at the time of admission to show their true current value. Any profit or loss on revaluation is distributed among the old partners in their old profit-sharing ratio.
• Adjustment of Capitals: Partners' capital accounts may be adjusted to be in proportion to the new profit-sharing ratio.

These adjustments ensure a fair transition when a new partner joins the firm.