New Profit-Sharing Ratio and Gaining Ratio

When a partner retires, his share of future profits does not simply vanish — it is picked up by the continuing partners, in whatever proportion they agree upon (or, if nothing is agreed, in their own existing ratio). Exactly which proportion this happens in must be worked out before any goodwill or revaluation adjustment can be completed, since goodwill and revaluation both depend on knowing who has gained, and by how much.

How the retiring partner's share is usually taken up

• The continuing partners acquire the retiring partner's share in their existing old ratio — the default assumption whenever the question does not state otherwise; in this special case, the gaining ratio and the (continuing partners') old ratio turn out to be identical.
• The continuing partners acquire it in a specified ratio — the retiring partner's vacated share is then divided between them in that stated ratio.
• A new ratio is given directly — the continuing partners' new shares are stated outright, and the gaining ratio must then be worked out by comparing each partner's new share with his old share.

Worked illustration. X, Y and Z share profits equally (1:1:1). Y retires, and X and Z agree to continue sharing profits equally between themselves.

X's old share = 1/3. X's new share = 1/2. X's gain = 1/2 − 1/3 = 1/6.

Z's old share = 1/3. Z's new share = 1/2. Z's gain = 1/2 − 1/3 = 1/6. …