Question

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

Answer 1

Old ratio (A: B: C) = 4: 3: 2

D is admitted for 1/3 share of profit

Let the combined share of profit of A, B, C and D be = 1

Combined share of A, B and C after D's admission = 1 - D's share

= 1 - 1/3

= 2/3

New ratio = Old ratio - Combined share of A ad B and C

A's share = 4/9 X 2/3 = 8/27

B's share = 3/9 X 2/3 = 6/27

C's share = 2/9 X 2/3 = 4/27

Sacrificing ratio = Old ratio - New ratio

A's share = 4/9 - 8/27 = 4/27

B's share = 3/9 - 6/27 = 3/27

C's share = 2/9 - 4/27 = 2/27

Sacrificing ratio (A: B: C) = 4/27: 3/27; 2/27

=4: 3: 2