When a new partner is admitted, the existing partners surrender a fraction of their profit share in favor of the new partner. The ratio in which they surrender their shares is called the Sacrificing Ratio (SR):
$$\text{Sacrificing Ratio} = \text{Old Share} - \text{New Share}$$Standard Calculation Cases:
- Case 1: When New Partner acquires share from old partners in their old ratio:
Let total profit $= 1$. Remaining share $= 1 - \text{New Partner's Share}$. Each old partner's new share $= \text{Old Share} \times \text{Remaining Share}$. Here, Sacrificing Ratio = Old Ratio. - Case 2: When New Partner acquires share in a specified ratio:
Sacrifice of Old Partner $= \text{New Partner's Share} \times \text{Fraction Surrendered}$.
New Share $= \text{Old Share} - \text{Sacrifice}$.