Question

A, B and C are partners sharing profits in the ratio of 2 : 2 : 1. D is admitted as a new partner for 1/6th share. C will retain his original share. Calculate the new profit-sharing ratio and sacrificing ratio.

Answer 1

Calculation of New Profit Sharing Ratio
A : B : C = 2 : 2 : 1 (Old Ratio)
D is admitted for `1/6`th share while C will continue to retain his original share `(1/5)`
Remaining Share = 1 - `1/6 - 1/5 = [ 30 - 5 - 6]/30 = 19/30`

This remaining share will be shared by A and B in the ratio of 2 : 2 (Old Ratio)*
A's New Share = `19/30 xx 2/4 = 38/120`

B's New Share = `19/30 xx 2/4 = 38/120`

C's New Share = `1/5 xx 24/24 = 24/120`

D's New Share = `1/6 xx 20/20 = 20/120`

A : B : C : D = 38 : 38 : 24 : 20 = 19 : 19 : 12 : 10 

*Since nothing is mentioned about the sacrifice made by the existing partners, it is assumed that A and B sacrifice in their old ratio.
Calculation of Sacrificing Ratio :
Sacrificing Ratio = Old Ratio - New Ratio
A's Sacrificing Share = `2/5 - 19/60 = [24 - 19]/60 = 5/60`

B's Sacrificing Share = `2/5 - 19/60 = [24 - 19]/60 = 5/60`

A : B = 5 : 5 or 1 : 1.