A, B, and C were in partnership, sharing profits in the ratio of 3:2:1 respectively, B retires and the new profit sharing ratio between A and C is 3:2. The gaining ratio is:

3:7

The correct answer is option 1- 3:7.

Old ratio = 3:2:1 (A, B and C)
B retires
New ratio = 3 : 2 (A & C)

Gained share = New share - Old share

A's gained share = 3/5 - 3/6
                        = (18-15)/30
                        = 3/30 

B's gained share = 2/5 - 1/6
                        = (12-5)/30
                        = 7/30 

Gaining ratio = 3/30 : 7/30
                    = 3:7