X and Y were sharing profit and loss of the business in the ratio of 3 : 2. They decided to admit Z, who will get $$\frac{1}{3}$$ of X share of profit form X and $$\frac{1}{2}$$ of Y share of profit from Y. New profit sharing ratio will be

The correct answer is D.

Initially, X and Y shared the profit in the ratio of 3 : 2. This means that X got 3 parts of the profit and Y got 2 parts of the profit.

When Z was admitted, X gave $\frac{1}{3}$ of his share to Z and Y gave $\frac{1}{2}$ of his share to Z. This means that X now gets 3 – $\frac{1}{3} = \frac{8}{3}$ parts of the profit and Y now gets 2 – $\frac{1}{2} = \frac{3}{2}$ parts of the profit.

The new profit sharing ratio is $\frac{8}{3} : \frac{3}{2} : 1 = 3 : 2 : 2$.

Option A is incorrect because it gives Z a share of 5 parts of the profit. This is not possible because the total number of parts is only 6 (3 + 2 + 1).

Option B is incorrect because it gives Z a share of 2 parts of the profit. This is not possible because X and Y already have a share of 5 parts of the profit.

Option C is incorrect because it gives Z a share of 1 part of the profit. This is not possible because X and Y already have a share of 5 parts of the profit.