X and Y are partners in a firm sharing profit and losses in the ratio of 3:2. Z is admitted as partner in the firm for 1/6th share in profits. Z acquires his share from X and Y in the ratio of 2:1. What will be the new profit sharing ratio of partners?

44:31:15

The correct answer is option 2- 44:31:15.

Z's share = 1/6

(i) Calculation of Sacrifice share :
Sacrificing Ratio =  2:1 (X : Y)
X’s sacrifice = 2/3 of 1/6
                   = 2/18
Y’s sacrifice = 1/3 of 1/6
                   = 1/18

(ii) Calculation of New Profit Sharing Ratio :

New share = Old share – Sacrifice share
X’s new share = 3/5 – 2/18
                       = (54-10)/90
                       = 44/90

Y’s new share = 2/5 – 1/18
                       = (36-5)/90
                       = 31/90

Z’s new share = 1/6

New ratio among X, Y and Z = 44/90 : 31/90 : 1/6
                                             = 44/90 : 31/90 : 15/90
                                             = 44 : 31 : 15