A, B and C are sharing profits and losses in the ratio of 5:3:2. C retires. His share will be distributed between A and B equally. Calculate new ratio of A and B.

3:2

The correct answer is option 3- 3:2.

Old ratio = 5:3:2 (A, B & C)

C's share is distributed between other partners equally.
A gains = 2/10 x 1/2
            = 2/20
B gains = 2/10 x 1/2
            = 2/20

New share = Old share + Gaining share

A's new share = 5/10 + 2/20
                       = (10+2)/20
                       = 12/20

B's new share = 3/10 + 2/20
                       = (6+2)/20
                      = 8/20

New ratio = 12:8
                = 3:2