Question

A, B and C are partners sharing profits in the ratio of 4 : 3 : 2. D is admitted for 1/3rd share in future profits. What is the sacrificing ratio ?

Answer 1

Sacrificing Ratio is calculated as below

Explanation:

Ratio in which A, B and C share profits is given as 4:3:2.

D’s share of profit = 1/3 of profit

Combined share of A, B and C after D’s admission = 1 – D’ share

$\begin{aligned}&=1-\frac{1}{3}\\&=\frac{2}{3}\end{aligned}$

Calculation of new ratio:

New Ratio will be calculated as Old Ratio $\times$ Combined Share of A, B and C

A’s new share

$=\frac{4}{9} \times \frac{2}{3}=\frac{8}{27}$

B’s new share

$=\frac{3}{9} \times \frac{2}{3}=\frac{6}{27}$

C’s new share

$=\frac{2}{9} \times \frac{2}{3}=\frac{4}{27}$

Calculation of Sacrificing Ratio:

Sacrificing Ratio will be calculated as Old Ratio- New Ratio

A’s sacrifice

$=\frac{4}{9}-\frac{8}{27}=\frac{12-8}{27}=\frac{4}{27}$

B’s sacrifice

$=\frac{3}{9}-\frac{6}{27}=\frac{9-6}{27}=\frac{3}{27}$

C’s sacrifice

$=\frac{2}{9}-\frac{4}{27}=\frac{6-4}{27}=\frac{2}{27}$

Thus, Sacrificing ratio of A:B:C

$=\frac{4}{27}: \frac{3}{27}: \frac{2}{27} \text { or } 4: 3: 2$

Thus, the sacrificing ratio will become 4 : 3 : 2