Understanding Sacrificing Ratio in Partnerships

When a new partner joins an existing partnership firm, the profit-sharing arrangement changes. The existing partners, who were previously sharing the profits among themselves, now have to share profits with the new partner. This often means that the existing partners give up a part of their share to accommodate the new partner's claim on the profits.

What is the Sacrificing Ratio?

The sacrificing ratio is the ratio in which the old or existing partners give up their share of profits in favour of the incoming or new partner. Essentially, it represents the proportion by which the existing partners' profit shares are reduced upon the admission of a new partner.

Key points about the sacrificing ratio:

• It is calculated only at the time of a new partner's admission.
• It is used to distribute any **goodwill** brought in by the new partner in premium, or any accumulated profits/reserves that are adjusted at the time of admission.
• The calculation involves comparing the old profit-sharing ratio with the new profit-sharing ratio.

Calculating the Sacrificing Ratio

The formula to calculate the sacrificing ratio is:

$Sacrificing Ratio = Old Ratio - New Ratio$

In this formula:

• Old Ratio refers to the profit-sharing ratio of the existing partners before the admission of the new partner.
• New Ratio refers to the profit-sharing ratio of all partners (including the new partner) after the admission.

A positive result from this calculation indicates the extent to which an existing partner sacrifices their share. If the result is negative, it implies that the partner is gaining a share, which is termed the "Gaining Ratio".

Why Other Options Are Incorrect

• Gaining Ratio: This is the opposite of the sacrificing ratio. It's the ratio in which the remaining partners increase their share when one partner retires or is admitted (if they gain share from others). The question specifically asks about the loss in favour of a new partner.
• Equal Ratio: This implies partners share profits equally (e.g., 1:1:1). While the new ratio might sometimes become equal, the term "equal ratio" itself doesn't define the loss made by existing partners.
• Proportionate Ratio: This term is not standard in partnership accounting related to admission or profit sharing adjustments. Ratios are typically defined by specific proportions (like 2:1, 1:1) or based on sacrifice/gain.

Therefore, the ratio by which existing partners lose in favour of the new partner is correctly identified as the sacrificing ratio.