Question

P and Q are partners sharing profits in the ratio of 3 : 2. They admit R into partnership who acquires 1/5th of his share from P and 4/25th share from Q. Calculate New Profit-sharing Ratio and Sacrificing Ratio.

Answer 1

$\begin{array}{l}\text{Calulation of New Profit Sharing Ratio}\\ \text{P:Q}=\text{3:2 (Old Ratio)}\\ \text{R acquires}\frac{1}{5}\text{th of his share from P}\\ \text{And, Remaining}\frac{4}{5}\text{th}(1-\frac{1}{5})\text{of his share from Q.}\\ \text{If}\frac{4}{5}\text{th share of R}=\frac{4}{25}\\ \text{R's share}=\frac{4}{25}\times \frac{5}{4}=\frac{5}{25}\\ \text{P}\text{'}\text{s sacrifice}=\frac{1}{5}\times \frac{1}{5}=\frac{1}{25}\\ \text{Q}\text{'}\text{s sacrifice}=\frac{4}{25}\\ \text{P}\text{'}\text{s new share}=\frac{3}{5}-\frac{1}{25}=\frac{15-1}{25}=\frac{14}{25}\\ \text{Q}\text{'}\text{s new share}=\frac{2}{5}-\frac{4}{25}=\frac{10-4}{25}=\frac{6}{25}\\ \text{R}\text{'}\text{s new share}=\frac{1}{5}\times \frac{5}{5}=\frac{5}{25}\\ \text{P:Q:R}=14:6:5\\ \text{Sacrificing Ratio}=\text{1:4}\end{array}$