Question

P,Q and R were partners in a firm sharing profits in the ratio of 3:2:1. They admitted S as a new partner for 1/8th share which be acquired from the partners in their old ratio. Find out new ratio.

Answer 1

Calculation of Sacrificing Ratio :

P's sacrifice = $\frac{1}{8}\times \frac{3}{6}=\frac{3}{48}$

Q's sacrifice = $\frac{1}{8}\times \frac{2}{6}=\frac{2}{48}$

R's sacrifice = $\frac{1}{8}\times \frac{1}{6}=\frac{1}{48}$

New ratio =Old ratio - Sacrificing ratio

P's new ratio=$\frac{3}{6}-\frac{3}{48}=\frac{(24-3)}{48}=\frac{21}{48}$

Q's new ratio=$\frac{2}{6}-\frac{2}{48}=\frac{(16-2)}{48}=\frac{14}{48}$

R's new ratio=$\frac{1}{6}-\frac{1}{48}=\frac{(8-1)}{48}=\frac{7}{48}$

S's ratio=$\frac{1}{8}\times \frac{6}{6}=\frac{6}{48}$

New ratio $=21:14:7:6$