AccountancyCBSE Class 12 · Reconstitution of a Partnership Firm – Retirement/Death of a Partner

Gaining Ratio Class 12: Formula, New Ratio and Solved Retirement Questions

Updated 15 October 2026 · Fact-checked

Gaining ratio is the ratio in which the continuing partners gain the share of profit given up by a retiring or deceased partner. Each partner's gain is his new share minus his old share. It is used to debit the continuing partners for the outgoing partner's share of goodwill, and it equals their old ratio if nothing else is agreed.

Understand Gaining Ratio

Meaning. When a partner retires or dies, his share of future profit is taken over by the continuing partners. The ratio in which they acquire it is the gaining ratio:

Gain = New share − Old share.

Why it matters. The continuing partners gain future profits that partly come from the firm's goodwill. They compensate the outgoing partner for his share of goodwill in the gaining ratio: Continuing Partners' Capital A/cs Dr (gaining ratio); To Retiring Partner's Capital A/c. The gaining ratio also decides who bears adjustments when a reserve or revaluation is handled 'without altering book values'.

Four ways a question gives the information.
1. Nothing said: continuing partners keep their old ratio; gaining ratio = old ratio of the continuing partners.
2. Retiring share taken in a stated ratio (say 2 : 1): gaining ratio = that ratio; new share = old share + gain.
3. Specific portions purchased (A takes 1/5, C takes 1/10): gaining ratio = 1/5 : 1/10; new share = old share + portion.
4. New ratio given: compute new − old for each continuing partner.

A trap: a continuing partner can sacrifice. If the agreed new ratio gives a continuing partner less than before, his new − old is negative: he sacrifices. The gaining partner then compensates both the retiring partner and the sacrificing continuing partner for goodwill.

Sacrificing ratio vs gaining ratio.

Sacrificing ratio: old − new; used on admission (and change in ratio); decides who receives goodwill.
Gaining ratio: new − old; used on retirement or death; decides who pays for goodwill.

Check. New shares of the continuing partners must add up to 1, and the total gain must equal the outgoing partner's old share.

Gaining Ratio: key facts

Gain of a continuing partner: New share − Old share; Negative result means he sacrifices.
Nothing agreed: Gaining ratio = old ratio of the continuing partners
Share taken in a ratio: New share = Old share + Retiring share × his proportion
Goodwill compensation: Retiring partner's share of goodwill = Firm's goodwill × his old share; debited to gainers in gaining ratio
Check: Σ gains = outgoing partner's old share; Σ new shares = 1

How to answer Gaining Ratio questions

Convert every share to a common denominator before subtracting; most mistakes in this topic are fraction slips.

1Write each partner's old share as a fraction with a common denominator.
2Identify the case: nothing said, share taken in a ratio, portions purchased, or new ratio given.
3Find the new share of each continuing partner.
4Gain = new − old; reduce the gains to the simplest ratio.
5Check that gains add up to the outgoing partner's share and new shares add up to 1.
6If a partner's gain is negative, treat him as a sacrificing partner when adjusting goodwill.

Gaining Ratio in real life

The idea, met in an everyday situation. Answer the question in your own words, then compare with the model answer. The one-line hook is what to remember.

Gaining ratio decides who pays the retiring partner

Suppose Asha, Bilal and Charu run a travel agency, sharing profits 2 : 2 : 1. Charu retires to study abroad. Asha and Bilal will continue to share profits equally. The agency's goodwill is valued at ₹1,50,000.

How much is Charu's share of goodwill, and how much must each continuing partner pay her?

Try it first, then show the solutionSolution

Charu's share of goodwill = 1,50,000 × 1/5 = ₹30,000.
Asha and Bilal continue in their old ratio 1 : 1, so the gaining ratio is 1 : 1.
Each is debited ₹15,000 and Charu is credited ₹30,000.

Answer: Charu's share is ₹30,000. Asha's Capital A/c Dr 15,000; Bilal's Capital A/c Dr 15,000; To Charu's Capital A/c 30,000. They pay because each now earns a bigger slice of the future profit Charu helped create.

Memory hook: Whoever gains the share pays for the goodwill.

Tricks to remember Gaining Ratio

Short memory aids. Say each one aloud once, then use it on a question the same day.

N − O = G
New minus Old equals Gain; Old minus New equals Sacrifice. Swap the order, swap the name.
Use it when: Avoiding sign errors.
Retire → Gain, Admit → Sacrifice
On retirement the stayers gain; on admission the old partners sacrifice.
Use it when: Choosing the right ratio.
Silent question, old ratio
If the new ratio is not given, gaining ratio = old ratio of the remaining partners.
Use it when: 1-mark MCQs.

Gaining Ratio: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Nothing agreed · 1 mark · MCQBoard level

A, B and C share profits 3 : 2 : 1. C retires. The gaining ratio of A and B is:
(a) 1 : 1
(b) 3 : 2
(c) 2 : 3
(d) 3 : 1

Try it first, then show the solutionSolution

No new ratio is given, so A and B continue in 3 : 2; the gaining ratio is their old ratio.

Answer: (b) 3 : 2

Example 2: Retiring share taken in a stated ratio · 3 marks · Short answerBoard level

A, B and C share profits 5 : 3 : 2. B retires and his share is taken by A and C in the ratio 2 : 1. Calculate the new profit sharing ratio and the gaining ratio. (3 marks)

Try it first, then show the solutionSolution

B's share 3/10: A takes 3/10 × 2/3 = 2/10; C takes 3/10 × 1/3 = 1/10.
New: A = 5/10 + 2/10 = 7/10; C = 2/10 + 1/10 = 3/10.
Gaining ratio = 2/10 : 1/10 = 2 : 1.

Answer: New ratio A : C = 7 : 3; gaining ratio 2 : 1.

Example 3: New ratio given · 3 marks · Short answerHarder board level

P, Q and R share profits 4 : 3 : 2. Q retires; P and R agree to share future profits 5 : 4. Calculate the gaining ratio. (3 marks)

Try it first, then show the solutionSolution

P: 5/9 − 4/9 = 1/9.
R: 4/9 − 2/9 = 2/9.
Gaining ratio = 1 : 2 (check: 1/9 + 2/9 = 3/9 = Q's share).

Answer: Gaining ratio P : R = 1 : 2.

Example 4: Specific portions purchased · 3 marks · Short answerHarder board level

A, B and C share profits 1/2, 3/10 and 1/5. B retires; A purchases 1/5 of the firm's profit from him and C the remaining 1/10. Calculate the new ratio and the gaining ratio. (3 marks)

Try it first, then show the solutionSolution

A = 1/2 + 1/5 = 7/10; C = 1/5 + 1/10 = 3/10.
New ratio = 7 : 3.
Gaining ratio = 1/5 : 1/10 = 2 : 1.

Answer: New ratio 7 : 3; gaining ratio 2 : 1.

Example 5: A continuing partner sacrifices · 4 marks · Short answerHOTS / competency

A, B and C share profits 6 : 3 : 1. C retires; A and B agree to share future profits equally. The firm's goodwill is valued at ₹1,00,000. Calculate each continuing partner's gain or sacrifice and pass the journal entry for goodwill. (4 marks)

Try it first, then show the solutionSolution

A: 5/10 − 6/10 = −1/10 (sacrifice). B: 5/10 − 3/10 = +2/10 (gain).
B gains 2/10 of goodwill = ₹20,000.
C is owed 1/10 × 1,00,000 = ₹10,000; A is owed 1/10 × 1,00,000 = ₹10,000.
B's Capital A/c Dr 20,000 To C's Capital A/c 10,000; To A's Capital A/c 10,000.

Answer: A sacrifices 1/10, B gains 2/10. B's Capital A/c Dr ₹20,000; To C's Capital A/c ₹10,000; To A's Capital A/c ₹10,000.

Example 6: Purpose of the gaining ratio · 1 mark · Assertion-reasonHOTS / competency

Assertion (A): On the retirement of a partner, his share of goodwill is debited to the continuing partners in their gaining ratio.
Reason (R): The continuing partners acquire the retiring partner's share of future profits.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.

Try it first, then show the solutionSolution

Those who gain future profit pay for it, in proportion to the gain. R explains A.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Where students lose marks in Gaining Ratio

The slips examiners see most often, and what to write instead.

Mistake: Subtracting in the wrong order
Reusing the sacrificing ratio formula.
Wrong working
Gain of P = 4/9 − 5/9 = −1/9
Right working
Gain of P = 5/9 − 4/9 = 1/9
Do this: Gain = New − Old.
Usually costs: 1 mark.
Mistake: Not using a common denominator
Subtracting fractions with different bases.
Wrong working
A's gain = 1/2 − 3/5 read as 2/3
Right working
1/2 − 3/5 = 5/10 − 6/10 = −1/10
Do this: Convert all shares to the same denominator first.
Usually costs: 1-2 marks.
Mistake: Ignoring a continuing partner's sacrifice
Assuming every continuing partner gains.
Wrong working
B and A both debited for C's goodwill.
Right working
A sacrifices; only B is debited, and A is credited along with C.
Do this: Check the sign of every new − old.
Usually costs: 2 marks.
Mistake: Writing the gaining ratio as the new ratio
Confusing two different ratios.
Wrong working
Gaining ratio = 7 : 3 (the new ratio).
Right working
Gaining ratio = 2 : 1 (the gains only).
Do this: Name each ratio in your answer.
Usually costs: 1 mark.

Exam tips

Show every step as fractions with a common denominator; it earns method marks even if you slip later.
State the case: 'In the absence of any agreement, the gaining ratio is the old ratio'.
Verify with Σ gains = outgoing partner's share in a bracket after the answer.
Gaining ratio is a frequent 1-mark MCQ and a step in 4- and 6-mark retirement questions.

Practice questions on Gaining Ratio

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · MCQBoard level
Gaining ratio is calculated as:
(a) old share − new share
(b) new share − old share
(c) new share ÷ old share
(d) old share ÷ new share
Hint
What is acquired.
Answer
(b) new share − old share
Q2 · 1 mark · MCQBoard level
A, B and C share profits 2 : 2 : 1. C retires. If nothing is agreed, the gaining ratio of A and B is:
(a) 2 : 1
(b) 1 : 2
(c) 1 : 1
(d) 2 : 2 : 1
Hint
Old ratio of A and B.
Answer
(c) 1 : 1
Q3 · 3 marks · Short answerBoard level
X, Y and Z share profits 3 : 2 : 1. X retires and his share is taken by Y and Z equally. Calculate the new ratio and the gaining ratio. (3 marks)
Hint
X's 3/6 is split in half.
Answer
Each gains 3/12. Y = 4/12 + 3/12 = 7/12; Z = 2/12 + 3/12 = 5/12. New ratio 7 : 5; gaining ratio 1 : 1.
Q4 · 3 marks · Short answerHarder board level
A, B and C share profits 2 : 3 : 5. A retires; B and C agree to share future profits 2 : 3. Calculate the gaining ratio. (3 marks)
Hint
Tenths.
Answer
B: 4/10 − 3/10 = 1/10; C: 6/10 − 5/10 = 1/10. Gaining ratio 1 : 1.
Q5 · 3 marks · Short answerHarder board level
P, Q and R share profits 3 : 2 : 1. R retires; his share is taken by P and Q in the ratio 1 : 2. Calculate the new ratio and the gaining ratio. (3 marks)
Hint
R's 1/6 is split 1/18 and 2/18.
Answer
P = 9/18 + 1/18 = 10/18; Q = 6/18 + 2/18 = 8/18. New ratio 5 : 4; gaining ratio 1 : 2.
Q6 · 1 mark · Very short answerHarder board level
M, N and O share profits 4 : 3 : 2. O dies. What is the gaining ratio of M and N if nothing is agreed, and why? (1 mark)
Hint
Old ratio of continuing partners.
Answer
4 : 3, because M and N continue in their old ratio and take O's share in that ratio.
Q7 · 3 marks · Short answerHarder board level
A, B and C share profits 3 : 2 : 1. B retires; the firm's goodwill is ₹1,20,000. A and C continue in their old ratio. Pass the journal entry for goodwill. (3 marks)
Hint
B's share is 2/6.
Answer
B's share = 1,20,000 × 2/6 = ₹40,000; gaining ratio 3 : 1. A's Capital A/c Dr 30,000; C's Capital A/c Dr 10,000; To B's Capital A/c 40,000.
Q8 · 1 mark · Assertion-reasonHarder board level
Assertion (A): The gaining ratio always equals the old ratio of the continuing partners.
Reason (R): Continuing partners may agree to share future profits in any new ratio.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Hint
'Always' is the trap.
Answer
(d) A is false, but R is true.
Q9 · 4 marks · Short answerHOTS / competency
A, B and C share profits 5 : 3 : 2. A retires; B and C agree on a new ratio of 2 : 3. The firm's goodwill is ₹2,00,000. Calculate the gaining ratio and pass the goodwill entry. (4 marks)
Hint
B gains 1/10, C 4/10.
Answer
B: 4/10 − 3/10 = 1/10; C: 6/10 − 2/10 = 4/10; gaining ratio 1 : 4. A's share = 2,00,000 × 5/10 = ₹1,00,000. B's Capital A/c Dr 20,000; C's Capital A/c Dr 80,000; To A's Capital A/c 1,00,000.
Q10 · 4 marks · Short answerHOTS / competency
L, M and N share profits 7 : 2 : 1. N retires; L and M agree to share future profits 3 : 2. The firm's goodwill is ₹1,50,000. Pass the journal entry for goodwill. (4 marks)
Hint
Check L's new − old.
Answer
L: 6/10 − 7/10 = −1/10 (sacrifice); M: 4/10 − 2/10 = +2/10 (gain). M pays 2/10 × 1,50,000 = ₹30,000: N is owed ₹15,000 and L ₹15,000. M's Capital A/c Dr 30,000 To N's Capital A/c 15,000; To L's Capital A/c 15,000.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.Formula for a partner's gain?Show answer
New share − Old share.
2.Which ratio is used to debit continuing partners for goodwill on retirement?Show answer
The gaining ratio.
3.A, B and C share 5 : 3 : 2; C retires, nothing agreed. Gaining ratio?Show answer
5 : 3.
4.What must the gains add up to?Show answer
The outgoing partner's old share.
5.Can a continuing partner sacrifice on retirement?Show answer
Yes, if the new ratio gives him less than his old share.

Gaining Ratio: frequently asked questions

What is the gaining ratio in Class 12 Accountancy?

The ratio in which continuing partners acquire the share of an outgoing partner; each partner's gain is new share minus old share.

How is the gaining ratio different from the sacrificing ratio?

Gaining ratio (new − old) is used on retirement or death to decide who pays for goodwill; sacrificing ratio (old − new) is used on admission to decide who receives the premium.

What if the new ratio is not given on retirement?

The continuing partners share in their old ratio, so the gaining ratio equals their old ratio.

What if a partner's gain comes out negative?

He has sacrificed; he is credited for goodwill along with the retiring partner, and the gaining partner pays both.