What is sacrificing ratio formula?

When a partnership firm decides to admit a new partner into their firm, the old partners have to forego a part of their share for the new partner. Therefore, sacrificing Ratio is the proportion in which the existing partners of a company give up a part of their share for the new partner. The partners can choose to forego their shares equally or in an agreed proportion.

Before admission of the new partner, the existing partners would be sharing their profits in the old ratio. Upon admission, the profit-sharing ratio would change to accommodate the new partner. This would give rise to the new ratio. Hence Sacrificing ratio formula can be calculated as:
Sacrificing Ratio = Old Ratio – New Ratio

To further understand the formula, let’s say Bruce and Barry are sharing a pizza of 6 slices equally (3 slices each). They decide to share their pizza with Arthur such that they all get equal slices (2 slices each). Hence, we can use the formula to calculate their sacrifice as follows:
Bruce’s sacrifice = 3 – 2 = 1 slice
Barry’s sacrifice = 3 – 2 = 1 slice

Therefore, their sacrificing ratio = 1:1. In this same way, we can solve various problems to calculate the sacrifice of partners during a change in their profit sharing ratio.

For example, Joshua and Edwin are partners, sharing profits in the ratio 7:3. They admit Adam into their partnership such that the new profit-sharing ratio is 5:2:3. Therefore, their sacrificing ratio can be calculated as:
Joshua’s sacrifice = old share – new share = 7/10 – 5/10 = 2/10
Edwin’s sacrifice = old share – new share = 3/10 – 2/10 = 1/10

Hence, sacrificing ratio of Joshua and Edwin is 2:1. Once the denominators are equal, we ignore them and only consider numerators while showing sacrificing ratio.