Financial Accounting · Retirement of Partner

New Profit Sharing Ratio and Gaining Ratio on Retirement

Updated 10 October 2026 · Fact-checked

When a partner retires, the continuing partners take over his share. The new ratio is each partner's old share plus the share he gains. Gaining ratio = New share − Old share for each continuing partner. It is used to charge the retiring partner's goodwill to the continuing partners.

Understand New Profit Sharing Ratio and Gaining Ratio

A firm is a group of partners sharing profit in an agreed ratio. When one partner retires, his share of profit does not disappear. Someone must take it. The continuing partners take it, and their shares go up.

The new profit sharing ratio is the ratio in which the continuing partners share profit after the retirement. The question may give it directly, or it may tell you how the retiring partner's share is taken over. For example, it may say the share is taken equally, in the old ratio, or in a stated ratio.

The gaining ratio is the ratio of the shares the continuing partners gain. Gain = New share − Old share. A partner who ends up with a bigger share has gained. The gaining ratio is the ratio of these gains.

Why does it matter? The retiring partner is entitled to his share of goodwill. The continuing partners pay for it, and they pay in proportion to what they gain. So the goodwill adjustment entry uses the gaining ratio, not the old ratio or the new ratio.

Sacrificing ratio and gaining ratio are mirror ideas. Sacrificing ratio is used on admission: old partners give up a share, so Sacrifice = Old share − New share. Gaining ratio is used on retirement: continuing partners take up a share, so Gain = New share − Old share.

Key rules to remember

Gain of a continuing partner: Gain = New share − Old share; Work with fractions on a common denominator. The gain is positive for a continuing partner on retirement.
Gaining ratio: Gaining ratio = Gain of A : Gain of B : Gain of C ...; Simplify the ratio of gains. The sum of all gains equals the retiring partner's old share.
Retiring partner's share taken over in a stated ratio: New share = Old share + (Retiring partner's share × Ratio in which it is taken); Use when the question says the share is acquired in a ratio, such as equally or 3 : 2.
Share taken in the old ratio: New ratio = Old ratio of continuing partners; If the retiring partner's share is taken in the old ratio, the gaining ratio is also the old ratio of the continuing partners, and the new ratio equals that old ratio.
Check: Sum of new shares = 1; Sum of gains = Retiring partner's old share; Always verify both checks before moving on.
Sacrificing ratio (for contrast): Sacrifice = Old share − New share; Used on admission of a partner, not on retirement.

How to solve New Profit Sharing Ratio and Gaining Ratio questions

Follow the same sequence for every question on this topic. It works whether the new ratio is given or has to be found.

1Write the old shares of all partners as fractions with a common denominator.
2Identify the retiring partner and his share.
3Find the new shares. If the new ratio is given, convert it into fractions. If the share is taken in a stated ratio, split the retiring partner's share in that ratio and add it to the old shares.
4Check that the new shares add up to 1.
5Calculate each continuing partner's gain = New share − Old share.
6Write the gaining ratio by simplifying the gains. Check that the total gain equals the retiring partner's old share.
7Use the gaining ratio for the goodwill adjustment entry: debit the gaining partners' capital accounts and credit the retiring partner's capital account.

Quickest way: Common denominator shortcut

When to use it: Use when the new ratio is given and the old ratio is given. It saves time in MCQs.

Convert the old and new ratios into fractions over their own totals.
Convert both to one common denominator (the product or LCM of the two totals).
Subtract old numerator from new numerator for each continuing partner. The resulting numerators are the gaining ratio directly.
If the retiring partner's share is taken in the old ratio, skip the subtraction: gaining ratio = old ratio of the continuing partners.
If the share is taken equally, the gains are equal, so the gaining ratio is 1 : 1 (for two continuing partners).

Common mistakes in New Profit Sharing Ratio and Gaining Ratio

Using the old ratio of all partners, including the retiring partner, to compute the new ratio.
Students forget that the retiring partner has left and the new ratio covers only the continuing partners.
Fix: Remove the retiring partner first. Then decide how his share is added to the others.
Calculating Old share − New share, as on admission.
Students mix up sacrificing ratio and gaining ratio.
Fix: On retirement, the continuing partners gain. Use New share − Old share. Gains must come out positive.
Assuming the new ratio equals the gaining ratio.
Both are ratios among the same continuing partners, so they look alike.
Fix: They are equal only in special cases. The gaining ratio is the ratio of the gains. The new ratio is the ratio of the final shares. Always compute the gains.
Comparing ratios without a common denominator.
Students subtract numerators of fractions that have different denominators, or compare ratios directly.
Fix: Convert every share to fractions over the same denominator before subtracting.
Dividing the retiring partner's share in the wrong ratio.
Students split it in the new ratio, or in the old ratio, when the question gives a different one.
Fix: Read the wording carefully. Split the retiring partner's share exactly in the ratio stated and add it to the old share.
Using the old ratio instead of the gaining ratio for the goodwill entry.
Students remember the old ratio from admission and revaluation problems.
Fix: Retiring partner's goodwill is borne by gaining partners in the gaining ratio. Use the old ratio only for revaluation and reserve adjustments.

Worked examples

Example 1

A, B and C share profit in the ratio 5 : 3 : 2. C retires. A and B agree to share future profit in the ratio 3 : 2. Find the gaining ratio.

Show the solution

Old shares: A = 5/10, B = 3/10, C = 2/10.
New shares: A = 3/5 = 6/10, B = 2/5 = 4/10. Total = 10/10, which is correct.
Gain of A = 6/10 − 5/10 = 1/10.
Gain of B = 4/10 − 3/10 = 1/10.
Check: total gain = 2/10, which equals C's old share.
Gaining ratio = 1/10 : 1/10 = 1 : 1.

Answer: Gaining ratio of A and B is 1 : 1. If the firm's goodwill is ₹60,000, C's share is 2/10 × 60,000 = ₹12,000. A and B bear it in 1 : 1, so ₹6,000 each.

Example 2

X, Y and Z share profit in the ratio 4 : 3 : 2. Z retires. X and Y take over Z's share in the ratio 2 : 1. Find the new profit sharing ratio and the gaining ratio.

Show the solution

Old shares: X = 4/9, Y = 3/9, Z = 2/9.
Z's share of 2/9 is taken in the ratio 2 : 1. X gets 2/3 of 2/9 = 4/27. Y gets 1/3 of 2/9 = 2/27.
Convert old shares to 27ths: X = 12/27, Y = 9/27.
New share of X = 12/27 + 4/27 = 16/27.
New share of Y = 9/27 + 2/27 = 11/27.
Check: 16/27 + 11/27 = 27/27 = 1.
New ratio = 16 : 11.
Gains: X = 4/27, Y = 2/27. Check: total = 6/27 = 2/9, which equals Z's old share.
Gaining ratio = 4 : 2 = 2 : 1.

Answer: New profit sharing ratio of X and Y is 16 : 11. Gaining ratio is 2 : 1.

Exam tips

In MCQs, first check whether the share is taken in the old ratio. If it is, the gaining ratio is the old ratio of the continuing partners and you save time.
In written answers, show the fractions, the gains and the check that gains equal the retiring partner's share. These earn step marks even if a later figure goes wrong.
Read the wording on how the share is taken: equally, in the old ratio, or in a stated ratio. Each leads to a different working.
Carry the gaining ratio straight into the goodwill entry. Examiners often combine this topic with goodwill and capital account preparation.
State your final ratios clearly, labelled as new ratio and gaining ratio. Do not leave them unnamed.

Practice questions from Retirement of Partner

New Profit Sharing Ratio and Gaining Ratio: frequently asked questions

How do I calculate the gaining ratio on retirement of a partner?

Find each continuing partner's new share and old share. Subtract old from new to get his gain. The ratio of these gains is the gaining ratio. The gains should add up to the retiring partner's old share.

What is the difference between sacrificing ratio and gaining ratio?

Sacrificing ratio applies when a partner is admitted. Old partners give up part of their share, so Sacrifice = Old share − New share. Gaining ratio applies on retirement, where continuing partners take up the share, so Gain = New share − Old share.

When is the gaining ratio the same as the old ratio?

When the continuing partners take the retiring partner's share in their old ratio. In that case each gain is proportional to the partner's old share, so the gaining ratio equals the old ratio of the continuing partners.

Why is the gaining ratio used for goodwill on retirement?

The retiring partner is paid for his share of goodwill by the continuing partners. Each one pays in proportion to the extra share he gains. So their capital accounts are debited in the gaining ratio and the retiring partner's capital account is credited.