Question

X and Y are partners sharing profits in 5 : 3 ratio admitted Z for $\frac{1}{10}$ share which he acquired equally for X and Y. Calculate new profit sharing ratio.

Answer 1

Calculate sacrificing ratio, then new ratio (old ratio - sacrifice ratio)

Z's share = $\frac{1}{10}$

Acquired from X = $\frac{1}{10}\times \frac{1}{2}=\frac{1}{20}$

Acquired from Y = $\frac{1}{10}\times \frac{1}{2}=\frac{1}{20}$

Therefore, X's new share = $\frac{5}{8}-\frac{1}{20}=\frac{25-2}{40}=\frac{23}{40}$

Y's new share = $\frac{3}{8}-\frac{1}{20}=\frac{15-2}{40}=\frac{13}{40}$

Hence, New profit sharing ratio of X : Y : Z

$\frac{23}{40}:\frac{13}{40}:\frac{1}{10}$

or $\frac{23}{40}:\frac{13}{40}:\frac{4}{40}$

or 23 : 13 : 4