New Profit sharing ratio = Old share of profits + share of profits acquired from the retiring partner (gain).

There can be following cases:

Case 1

Suppose A, B and C are partners sharing in the ratio 3:2:1 and,

(a) A retires

(b) B retires

(c) C retires

Solution:

Old Profit ratio = 3:2:1

(a) A retires: new profit sharing ratio is 2:1

(b) B retires: new profit sharing ratio is 3:1

(c) C retires: new profit sharing ratio is 3:2

Case 2

Suppose A, B and C are partners sharing profits in the ratio 3:2:1. A retires and B takes 2/6th from A and C takes 1/6th from A.

B’s New Share = B’s old share + B’s gain (takes from A) = 2/6 + 2/6 = 4/6

C’s New Share = C’s old share + C’s gain (takes from A) = 1/6 + 1/6 = 2/6

New ratio of B and C = 2:1

Case 3

Suppose A, B and C are partners sharing profits in the ratio 3:2:1. B retires and his share is acquired by A and C in the ratio 3:1. Calculate new ratio.

Solution:

Share acquired by A = 2/6 × 3/4 = 6/24

Share acquired by C = 2/6 × 1/4 = 2/24

A’s New Share =A’s old share +A’s gain = 3/6 + 6/24 = 18/24

C’s New Share = C’s old share + C’s gain = 1/6+ 2/24 = 6/24

New ratio of A and C = 3:1