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

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 shares
= 1 - `1/3 = 2/3`

New Ratio = Old Ratio × combined share of A, B and C
A's = `4/9 xx 2/3 = 8/27`

B's = `3/9 xx 2/3 = 6/27`

C's = `2/9 xx 2/3 = 4/27`

New Ratio = `8/27 : 6/27 : 4/27 : 4/27 : 1/3`

= `8/27 : 6/27 : 4/27 : 4/27 : 9/27`

Sacrificing Ratio = Old Ratio − New Ratio
A's = `4/9 - 8/27 = 4/27`

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

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

Sacrificing Ratio = A : B : C

= `4/27 : 3/27 : 2/27`

=  4 : 3 : 2.