P, Q, R, S were partners sharing profits in the ratio 2:3:5:2. S retires and his share is acquired by Q and R in the ratio 3:2. calculate the new ratio

Hey

Here the old ratio of P, Q, R and S is: 2 : 3 : 5 : 2
S retires from the firm
His share i.e. $\frac{2}{12}$ is acquired by Q and R in the ratio of 3 : 2
Q's Gain = $\frac{3}{5}\times \frac{2}{12}=\frac{6}{60}$
R's Gain = $\frac{2}{5}\times \frac{2}{12}=\frac{4}{60}$
New Share = Old Share + Gaining Share

P's New Share = $\frac{2}{12}\times \frac{5}{5}=\frac{10}{60}$
Q's New Share = $\frac{3}{12}+\frac{6}{60}=\frac{15+6}{60}=\frac{21}{60}$
R's New Share = $\frac{5}{12}+\frac{4}{60}=\frac{25+4}{60}=\frac{29}{60}$

New Profit Sharing Ratio of P, Q and R will be 10 : 21 : 29