Question

A,B and C are partners sharing profits and losses in the ratio of 4:3:2. C retires from the business. A is acquiring 4/9 of C's share and balance is acquired by B. Calculate the new profit-sharing ratio and gaining ratio.

Answer 1

$A^{\prime }s$ Share $=\frac{2}{9}-\frac{4}{9}$

Old ratio $\begin{array}{ccc}A& B& C\\ 4& 3& 2\end{array}$

$C^{\prime }s$ share $=\frac{2}{9}$

$A^{\prime }s$ gain $=C^{\prime }s$ share $\times \frac{4}{9}$

$=\frac{2}{9}\times \frac{4}{9}=\frac{8}{81}$

$B^{\prime }s$ gain $=C^{\prime }s$ share $-A^{\prime }s$ gain

$=\frac{2}{9}-\frac{8}{81}=\frac{10}{81}$

New share $=$ old share $+$ gaining share

$A=\frac{4}{9}+\frac{8}{81}=\frac{44}{81}$

$B=\frac{3}{9}+\frac{10}{81}=\frac{37}{81}$

$\therefore$ New $PSR=\frac{44}{81}:\frac{37}{81}=44:37$