Q.Explain the meaning of Sacrificing Ratio. Under what circumstances can the sacrificing ratio be different from the old profit-sharing ratio of the partners?

Sacrificing ratio is the ratio in which the old partners give up a part of their old profit share for the new partner, and it is what decides how goodwill compensation is split among them.

When the new partner's share is simply deducted from the old partners' shares in their existing ratio, the sacrifice mirrors the old ratio. But when the new partner acquires their share from the old partners in some OTHER stated ratio, or when a new ratio is given directly that does not reduce each old partner's share proportionately, the sacrifice differs from partner to partner and no longer matches the old ratio — one partner may even sacrifice nothing while another bears the whole sacrifice.

Meaning of Sacrificing Ratio

When a new partner is admitted, they must be given a share of profits, and that share can only come out of what the old partners used to hold — the total of all shares must still add up to one whole. The Sacrificing Ratio is the ratio in which the old partners give up, or 'sacrifice', part of their former share of profit in favour of the new partner. For each old partner:

Sacrificing Share = Old Profit Share − New Profit Share

The ratio of these sacrificing shares, one partner to another, is the Sacrificing Ratio. Its main practical use is to decide how the new partner's premium for goodwill is divided among the old partners — it is always divided in the sacrificing ratio, because it is precisely for the share being sacrificed that the old partners are being compensated.

When does it equal the old ratio, and when does it differ?

If the new partner's share is simply subtracted from the old partners' shares IN THEIR OLD RATIO (the standard default when a question gives only the new partner's share and says nothing more), then each old partner's sacrifice works out to be proportional to their old share, and the Sacrificing Ratio turns out to be exactly the same as the Old Ratio.

However, the sacrificing ratio can and does differ from the old ratio in situations such as:

1. The new partner acquires their share from the old partners in a specified ratio that is different from the old partners' own ratio (for example, taking more from one partner than the other, in a ratio not equal to the old ratio).
2. The new profit-sharing ratio is given directly in the question (for all partners), and when compared with the old ratio, it does not represent a proportionate scaling-down of the old shares — one partner may sacrifice a larger portion relative to their old share than another, or one partner may not sacrifice at all while another gives up their entire reduction.
3. A partner's share does not decrease at all, or even increases slightly — in that rare case that partner has a 'gain' rather than a sacrifice, and is treated as having a negative sacrifice, meaning that partner may even have to compensate the OTHER old partners rather than receive compensation from the new partner.

Because of these possibilities, the sacrificing ratio must always be independently computed as (Old Share − New Share) for each old partner, and never simply assumed to be the same as the old profit-sharing ratio.

Students often assume the sacrificing ratio is ALWAYS the same as the old ratio without checking — always compute Old Share − New Share for each partner explicitly before concluding what the sacrificing ratio is. Another mistake is confusing sacrificing ratio with the new ratio when dividing goodwill — goodwill brought in by the new partner is always shared in the SACRIFICING ratio, not the new ratio.