Q.A, B and C share profits and losses in the ratio 3:2:1. B retires, and A and C decide to share the future profits of the firm equally. Calculate the new profit-sharing ratio and the gaining ratio of A and C.
Old ratio A:B:C = 3:2:1 (out of 6), so A's old share = 3/6 = 1/2, B's old share = 2/6 = 1/3, C's old share = 1/6.
New ratio (given): A and C share equally, so A's new share = 1/2 and C's new share = 1/2.
Gain of A = New Share − Old Share = 1/2 − 1/2 = Nil.
Gain of C = New Share − Old Share = 1/2 − 1/6 = 3/6 − 1/6 = 2/6 = 1/3.
(Independent check: A's gain (nil) + C's gain (1/3) = 1/3, which exactly equals B's old share of 1/3 — confirming the whole of B's vacated share has gone to C alone, and none of it to A.)
This is a genuinely important case to understand, not just calculate: a continuing partner's share can stay exactly the same even though a partner has retired, if the SPECIFIC new ratio agreed happens to leave that partner's proportion unchanged. Since A gains nothing, A need not compensate B for any goodwill either — the entire goodwill adjustment would fall on C alone in a case like this.
New profit-sharing ratio of A and C = 1 : 1. A's gain is Nil (his share stays at 1/2); C's gain is 1/3 (the whole of B's old share) — so the gaining ratio between A and C is entirely in C's favour, and only C bears the goodwill adjustment for B's retirement.
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