Profit Sharing, Sacrificing, and Gaining Ratio in Class 12 Accountancy

Profit sharing ratio, sacrificing ratio, and gaining ratio are small topics on paper, but they can decide whether a partnership question feels easy or confusing.

Many Class 12 Accountancy students try to memorise the formulas first. That works for one or two questions, but the confusion comes back when the question changes the wording. One question says a new partner is admitted. Another says an old partner retires. Another says partners change their existing ratio. Suddenly the same numbers start behaving differently.

The solution is to understand one simple idea:

Once this becomes clear, profit sharing ratio, sacrificing ratio, and gaining ratio stop feeling like three separate chapters. They become three connected ways of reading the same change.

Start With Profit Sharing Ratio

Profit sharing ratio is the ratio in which partners share the profits and losses of the firm.

If A and B share profits in the ratio of 3:2, it means:

Partner	Share of profit
A	3/5
B	2/5

This is the base of the question. Before admission, retirement, death, or change in ratio, always write the old profit sharing ratio clearly.

Students often make mistakes because they start calculating the new ratio before writing the old one. That is like solving a map question without knowing the starting point.

Why Ratios Change in Partnership Accounts

Ratios change when the agreement between partners changes.

This usually happens in three situations:

Situation	What changes
Admission of a partner	A new partner gets a share from old partners
Retirement or death of a partner	Continuing partners receive the outgoing partner’s share
Change in existing ratio	Partners continue, but their future shares change

In all three situations, someone may lose a portion of profit and someone may gain a portion of profit. Accountancy uses different names for these changes so that goodwill and other adjustments can be shared fairly.

Understand Sacrificing Ratio Before Memorising It

Sacrificing ratio is used when a partner gives up part of their profit share.

In admission of a new partner, the new partner gets a share in future profits. That share has to come from the old partners. The old partners who give up their share are called sacrificing partners.

The formula is simple:

Sacrifice = Old share - New share

The sacrificing ratio is the ratio of these sacrifices.

Let us make it practical.

Example 1: New Partner Admitted and Sacrifice Is in Old Ratio

A and B are partners sharing profits in the ratio of 3:2. They admit C for 1/5 share. The question does not say from whom C gets this share.

In such a case, we usually assume that A and B sacrifice in their old ratio.

Step 1: Write C’s share.

C's share = 1/5

Step 2: Find the remaining share for A and B.

Remaining share = 1 - 1/5 = 4/5

Step 3: Divide the remaining 4/5 between A and B in the old ratio 3:2.

Partner	New share
A	3/5 of 4/5 = 12/25
B	2/5 of 4/5 = 8/25
C	1/5 = 5/25

So the new profit sharing ratio is:

A : B : C = 12 : 8 : 5

Now calculate sacrifice:

Partner	Old share	New share	Sacrifice
A	3/5 = 15/25	12/25	3/25
B	2/5 = 10/25	8/25	2/25

So the sacrificing ratio is:

A : B = 3 : 2

This example looks simple because the sacrifice happened in the old ratio. But do not assume that every question will work like this.

Example 2: New Ratio Is Given Directly

Sometimes the question gives the old ratio and the new ratio. In that case, do not try to invent the sacrifice. Just compare old share with new share.

A and B share profits in the ratio of 5:3. They admit C, and the new ratio becomes 4:2:1.

Old ratio:

Partner	Old share
A	5/8
B	3/8

New ratio:

Partner	New share
A	4/7
B	2/7
C	1/7

Now compare only A and B because they are the old partners.

Partner	Old share	New share	Sacrifice
A	5/8	4/7	5/8 - 4/7 = 3/56
B	3/8	2/7	3/8 - 2/7 = 5/56

So the sacrificing ratio is:

A : B = 3 : 5

Notice something important. A and B’s old ratio was 5:3, but their sacrificing ratio became 3:5. This is why blindly using the old ratio can be risky.

What Gaining Ratio Really Means

Gaining ratio is the opposite idea.

It shows the ratio in which partners gain a share of profit. It is commonly used when a partner retires or dies, because the remaining partners receive the outgoing partner’s share.

The formula is:

Gain = New share - Old share

The gaining ratio is the ratio of these gains.

This is the easiest way to remember the difference.

Example 3: A Partner Retires

A, B, and C are partners sharing profits in the ratio of 3:2:1. C retires. A and B decide to share future profits in the ratio of 3:2.

Old shares:

Partner	Old share
A	3/6
B	2/6
C	1/6

New shares of A and B:

Partner	New share
A	3/5
B	2/5

Now compare A and B’s old shares with their new shares.

Partner	Old share	New share	Gain
A	3/6 = 15/30	3/5 = 18/30	3/30
B	2/6 = 10/30	2/5 = 12/30	2/30

So the gaining ratio is:

A : B = 3 : 2

Here the gaining ratio is the same as the new ratio between A and B because they took C’s share in the same proportion. But again, this is not always true. If the question says A and B acquire C’s share in a different ratio, the gaining ratio will follow that information.

A Simple Table to Avoid Confusion

Whenever you solve these questions, make this rough table first:

Partner	Old share	New share	Change
A	Write fraction	Write fraction	Old - New or New - Old
B	Write fraction	Write fraction	Old - New or New - Old
C	Write fraction if applicable	Write fraction if applicable	Check if partner is admitted or retiring

Then ask:

• Did this partner’s share reduce? That is sacrifice.
• Did this partner’s share increase? That is gain.
• Is this partner new? Their share came from old partners.
• Is this partner retiring? Their share went to continuing partners.

This table is slower in the beginning, but it makes you faster later because you stop guessing.

Where Goodwill Comes In

Goodwill is connected to these ratios because profit share has value.

When a new partner enters, old partners may lose a part of their future profit. So the new partner may compensate the sacrificing partners through goodwill. That compensation is shared by the old partners in their sacrificing ratio.

When a partner retires or dies, the continuing partners may gain a part of the outgoing partner’s share. So the gaining partners may compensate the outgoing partner for goodwill in the gaining ratio.

You do not need to fear the goodwill entries if the ratio is clear. Most confusion in goodwill treatment starts because the sacrificing or gaining ratio was calculated casually.

Common Mistakes Students Make

The first mistake is using the old profit sharing ratio automatically. The old ratio is only the starting point. It may or may not be the final answer.

The second mistake is mixing up sacrifice and gain. If the old share is bigger than the new share, the partner has sacrificed. If the new share is bigger than the old share, the partner has gained.

The third mistake is comparing ratios without converting them into fractions. For example, 3:2 and 4:3 cannot be compared directly. You must write them as shares of total profit.

The fourth mistake is ignoring the wording “from”, “equally”, “in the old ratio”, or “in the ratio of”. These words decide how the share moves between partners.

A Good Practice Method for the First Few Weeks

Do not start by solving only long admission or retirement questions. First build comfort with ratio movement.

Use this order:

1. Convert simple ratios into fractions.
2. Calculate new profit sharing ratio when a new partner is admitted.
3. Calculate sacrificing ratio from old and new shares.
4. Calculate gaining ratio when a partner retires.
5. Then connect the ratio to goodwill treatment.

Spend a little time on rough working. It may feel basic, but it builds the exact thinking needed for larger questions.

Frequently Asked Questions

What is profit sharing ratio in Class 12 Accountancy?

Profit sharing ratio is the ratio in which partners share the profits and losses of the firm. For example, if A and B share profits in 3:2, A gets 3/5 of the profit and B gets 2/5.

What is sacrificing ratio?

Sacrificing ratio is the ratio in which partners give up their share of profit in favour of another partner. It is commonly used when a new partner is admitted. The basic formula is old share minus new share.

What is gaining ratio?

Gaining ratio is the ratio in which partners receive an increase in their profit share. It is commonly used when a partner retires or dies. The basic formula is new share minus old share.

Is sacrificing ratio always the same as old profit sharing ratio?

No. It is the same as the old ratio only when the question says so or when the new partner takes the share from old partners in their old ratio. If the new ratio is given, calculate sacrifice by comparing old share and new share.

Is gaining ratio always the same as new profit sharing ratio?

No. It can be the same in some questions, but not always. The gaining ratio depends on how the continuing partners acquire the outgoing partner’s share.

How can I avoid mistakes in these ratios?

Write old shares and new shares as fractions, compare them carefully, and then decide whether each partner has sacrificed or gained. Do not jump directly to the final ratio without showing rough work.