The correct answer is: C. In their sacrificing ratio.
When a new partner is admitted into a firm, the old partners have to sacrifice their share of the profits to make room for the new partner. The amount of goodwill that the new partner brings in is used to compensate the old partners for their sacrifice. The old partners share the goodwill in the ratio of their sacrificing ratio.
The sacrificing ratio is the ratio in which the old partners’ capitals are reduced when a new partner is admitted into the firm. It is calculated by deducting the amount of goodwill brought in by the new partner from the old partners’ capitals.
For example, if a firm has three partners, A, B, and C, and the new partner brings in goodwill of $10,000, the sacrificing ratio would be:
A:B:C = (A’s capital – $10,000):(B’s capital – $10,000):(C’s capital – $10,000)
If A’s capital is $20,000, B’s capital is $30,000, and C’s capital is $40,000, the sacrificing ratio would be:
A:B:C = (20,000 – 10,000):(30,000 – 10,000):(40,000 – 10,000)
= 10,000:20,000:30,000
= 1:2:3
The old partners would share the goodwill in the ratio of 1:2:3.