Reconstitution of a Partnership Firm – Admission of a Partner

C’s share = $\frac{1}{4} = \frac{4}{16}$.

Remaining share for A and B = $1 - \frac{1}{4} = \frac{3}{4} = \frac{12}{16}$.

Old ratio of A:B = 3:1, so they share the remaining $\frac{12}{16}$ in the ratio 3:1.

- A’s share = $\frac{3}{4} \times \frac{3}{4} = \frac{9}{16}$
- B’s share = $\frac{3}{4} \times \frac{1}{4} = \frac{3}{16}$
- C’s share = $\frac{4}{16}$

So the new ratio is $9:3:4$. The printed options do not show this exact ratio; the book’s illustration, however, gives the method. Among the given options, none matches the correct ratio exactly.

X and Y share profits in the ratio 3:2, so their old shares are:
- X = $\frac{3}{5}$
- Y = $\frac{2}{5}$

Z gets $\frac{1}{5}$, and acquires:
- $\frac{3}{20}$ from X
- $\frac{1}{20}$ from Y

So new shares are:
- X = $\frac{3}{5} - \frac{3}{20} = \frac{12}{20} - \frac{3}{20} = \frac{9}{20}$
- Y = $\frac{2}{5} - \frac{1}{20} = \frac{8}{20} - \frac{1}{20} = \frac{7}{20}$
- Z = $\frac{1}{5} = \frac{4}{20}$

New profit sharing ratio = 9 : 7 : 4.

A and B share profits in the ratio 3:1.

Since nothing else is stated, the new partner is assumed to acquire his share from the old partners in their old ratio. Therefore, their sacrificing ratio is the same as the old ratio:

A : B = 3 : 1.

The chapter states that accumulated profits such as general reserve are distributed among the partners by transferring them to the old partners’ capital/current accounts in the old profit sharing ratio. The new partner is not entitled to them.