Question

A and B are partners sharing profits and losses in the ratio of 3:2. A surrenders $\frac{1}{2}$ of his share and B surrenders $\frac{1}{4}$ of his share in favour of C. Calculate new ratio.

Answer 1

Sacrificing ratio of $A=\frac{3}{5}\times \frac{1}{2}=\frac{3}{10}$

Sacrificing ratio of $B=\frac{2}{5}\times \frac{1}{4}=\frac{2}{20}$

New ratio =Old ratio -Sacrificing ratio

$A=\frac{3}{5}-\frac{3}{10}=\frac{(12-6)}{20}=\frac{6}{20}$

$B=\frac{2}{5}-\frac{2}{20}=\frac{(8-2)}{20}=\frac{6}{20}$

$C=\frac{3}{10}+\frac{2}{20}=\frac{(6+2)}{20}=\frac{8}{20}$

New ratio =6:6:8 or 3:3:4