Question

A and B were partners in a firm sharing profits and losses in the ratio of 3 : 2. They admit C as a new partner. The profit and loss sharing shall be so adjusted that A receives half of B's share and C receives one-third of A's share. Calculate new profit sharing ratio and sacrificing ratio.

Answer 1

Let B's new share be 1.

A's new share = $\frac{1}{2}$

C's new share = $\frac{1}{3}\times \frac{1}{2}=\frac{1}{6}$

New ratio = $\frac{1}{2}:1:\frac{1}{6}=3:6:1$

Sacrificing ratio = Old ratio - New ratio

A's sacrifice ratio = $\frac{3}{5}-\frac{3}{10}=\frac{(6-3)}{10}=\frac{3}{10}$

B's sacrifice ratio = $\frac{2}{5}-\frac{6}{10}=\frac{(4-6)}{10}=\frac{-2}{10}$