Question

X and Y are partners sharing profits and losses in the ratio of 3 : 2. They admit Z into partnership. X gives 1/3rd of his share while Y gives 1/10th from his share to Z. Calculate new profit-sharing ratio and sacrificing ratio.

Answer 1

Old Ratio of X and Y is 3 : 2.

$$\begin{gathered} \mathrm{X}\text{'}\mathrm{s}\mathrm{sacrifice}=\frac{1}{3}\times \frac{3}{5}=\frac{3}{15} \\ \mathrm{Y}\text{'}\mathrm{s}\mathrm{sacrifice}=\frac{1}{10} \\ \mathrm{Sacrificing}\mathrm{Ratio}=\frac{3}{15}:\frac{1}{10}\mathrm{or}2:1 \end{gathered}$$

New Ratio = Old Share − Share Sacrificed

$$\begin{gathered} \mathrm{X}\text{'}\mathrm{s}\mathrm{new}\mathrm{share}=\frac{3}{5}-\frac{3}{15}=\frac{6}{15} \\ \mathrm{Y}\text{'}\mathrm{s}\mathrm{new}\mathrm{share}=\frac{2}{5}-\frac{1}{10}=\frac{3}{10} \\ \mathrm{Z}\text{'}\mathrm{s}\mathrm{share}=\frac{3}{15}+\frac{1}{10}=\frac{9}{30} \\ \mathrm{New}\mathrm{Ratio}=\frac{6}{15}:\frac{3}{10}:\frac{9}{30}=4:3:3 \end{gathered}$$