Q.A and B share profits and losses in the ratio of 3 : 1, C is admitted into partnership for 1/4 share. The sacrificing ratio of A and B is:

Let’s start with something you already know from everyday life.

Suppose you and your friend share a pizza equally — half each. One day, your friend says, “I’m not that hungry, you can have a bigger slice today.” So you take 60% and your friend takes 40%. Your friend has sacrificed 10% of the pizza in your favour. That 10% is the sacrificing ratio — the share your friend gave up so you could have more.

Now bring this into a partnership firm. Partners share profits in a fixed ratio (say 3:2). When a new partner is admitted, the old partners have to give up a part of their share to make room for the newcomer. The proportion in which they give up their shares is called the sacrificing ratio.

Precise meaning

If the result is positive, that partner has sacrificed. If negative, that partner has gained (which is called the gaining ratio, used at retirement).

For example, if A and B share profits 3:2, and they admit C for a 1/5th share, the new ratio might become 2:2:1. Then:

• A’s sacrifice = 3/5 – 2/5 = 1/5
• B’s sacrifice = 2/5 – 2/5 = 0

So A alone sacrifices 1/5th of the total profit. That 1/5th is the sacrificing ratio between A and B — here it’s simply 1:0.

Why does it matter?

Because the new partner brings in goodwill (a premium) to compensate the old partners for the share they gave up. That goodwill is distributed among the sacrificing partners in their sacrificing ratio. If you don’t calculate the sacrificing ratio correctly, you’ll distribute the goodwill unfairly — and that’s a serious accounting error.

Accounting treatment

When the new partner brings in his share of goodwill in cash:

1. Journal entry:

   • Debit: Cash/Bank A/c (with the amount brought in)
   • Credit: Premium for Goodwill A/c (with the same amount)

2. Then the premium is distributed to the sacrificing partners:

   • Debit: Premium for Goodwill A/c
   • Credit: Old Partners’ Capital A/cs (individually, in sacrificing ratio)

If the new partner does not bring in cash, the adjustment is done through the capital accounts directly (the new partner’s capital is debited, and the old partners’ capitals are credited).

Format: Capital Accounts (showing goodwill adjustment) …