A and B are partner profit and loss in the ratio of 3 : 2. They admitted C as a new partner for 1/5 share in the future. Calculate new profit sharing Ratio.

12 : 8 : 5

The correct answer is Option (2) - 12 : 8 : 5.

Old ratio = 3:2 (A & B)
C admit with 1/5th share.
Let total share of firm = 1
C = 1/5
Remaining share = 1-1/5
                         = 4/5
This 4/5 is shared between A & B in their old ratio.
A's new share = 3/5 x 4/5
                     = 12/25

B's new share = 2/5 x 4/5
                     = 8/25

NEW RATIO = 12/25 : 8/25 : 1/5
                 = 12/25 : 8/25 : 5/25
                 = 12:8:5