A and B are partners in a firm sharing profits in the ratio of 3:2. They admit C as a partner for 1/3 share. the sacrificing ratio between A and B is:

3:2

The correct answer is option 1- 3:2.

Old ratio = 3:2 (A&B)
C admits = 1/3

Let total share = 1
C's share = 1/3
Remaining share = 1- 1/3
                         = 2/3

This 2/3 is divided between A & B in ratio of 3:2.

A's new share = 2/3 x 3/5
                     = 6/15

B's new share = 2/3 x 2/5
                     = 4/15

New ratio = 6/15 : 4/15 : 1/3
               = 6/15 : 4/15 :5/15
               = 6:4:5

SACRIFICED SHARE = OLD SHARE - NEW SHARE

Sacrifice of A = 3/5 - 6/15
                    = (9-6)/15
                    = 3/15

Sacrifice of B = 2/5 - 4/15
                    = (6-4)/15
                    = 2/15

Sacrificing ratio = 3/15 :2/15
                       = 3:2