$A$, $B$ and $C$ are partners sharing profits in the ratio of $3:2:1$. $A$ retires and his share is taken up by $B$ and $C$ in the ratio of $3:2$. Calculate the new profit sharing ratio.

Old profit sharing ratio of $A,B,C=3:2:1$$A$ 's share = $\frac{3}{6}$$A$ 's share is taken up by $B$ and $C$ in the ratio $3:2$.Share gained by $B=\frac{3}{6}\times \frac{3}{5}=\frac{9}{30}$ Share gained by $C=\frac{3}{6}\times \frac{2}{5}=\frac{6}{30}$ Now, compute new shares:$B$ 's New Share = Old Share + Gain = $\frac{2}{6}+\frac{9}{30}=\frac{10+9}{30}=\frac{19}{30}$$C$ 's New Share = Old Share + Gain = $\frac{1}{6}+\frac{6}{30}=\frac{5+6}{30}=\frac{11}{30}$ The new profit sharing ratio between $B$ and $C$ is $19:11$.