Question

P and Q are partners sharing profits in 2 : 1 ratio. They admitted R into partnership giving him $\frac{1}{5}$ share which he acquired from P and Q in 1 : 2 ratio. Calculate the new profit sharing ratio.

Answer 1

Old ratio of P and Q = 2 : 1

R's share = $\frac{1}{5}$

Contribution by P to R = $\frac{1}{5}\times \frac{1}{3}=\frac{1}{15}$

Contribution by Q to R = $\frac{1}{5}\times \frac{2}{3}=\frac{2}{15}$

(Old ratio - Sacrifice ratio = New ratio)

$\therefore$ P's new share = $\frac{2}{3}-\frac{1}{15}=\frac{10-1}{15}=\frac{9}{15}$

Q's new share = $\frac{1}{3}-\frac{2}{15}=\frac{5-2}{15}=\frac{3}{15}$

Hence, new profit sharing ratio of P : Q : R

$\frac{9}{15}:\frac{3}{15}:\frac{1}{5}$

or $\frac{9}{15}:\frac{3}{15}:\frac{3}{15}$

or 9 : 3 : 3

or 3 : 1 : 1