1 markMCQSection A

Dharam, Karam and Raman were partners in a firm sharing profits and losses in the ratio of 7 : 8 : 5. On 31st March, 2025, Raman retired from the firm. Dharam and Karam decided to share profits in future in the ratio of 11 : 9. Their gaining ratio will be : OR Deen, Raju and Hari were partners in a firm sharing profit and losses in the ratio of 7 : 6 : 7. On 31st March, 2025 Raju died. Deen and Hari decided to take over Raju's share equally. The new profit sharing ratio between Deen and Hari will be :

Q: Dharam, Karam and Raman were partners in a firm sharing profits and losses in the ratio of 7 : 8 : 5. On 31st March, 2025, Raman retired from the firm. Dharam and Karam decided to share profits in future in the ratio of 11 : 9. Their gaining ratio will be : OR Deen, Raju and Hari were partners in a firm sharing profit and losses in the ratio of 7 : 6 : 7. On 31st March, 2025 Raju died. Deen and Hari decided to take over Raju's share equally. The new profit sharing ratio between Deen and Hari will be :

**Correct option: (C) 4 : 1** Gaining Ratio = New Share − Old Share. $\text{Dharam gains } 11/20 - 7/20 = 4/20 \text{ and Karam gains } 9/20 - 8/20 = 1/20$, giving a gaining ratio of **4 : 1**.

Reconstitution of a Partnership Firm: Retirement/Death of a Partner

Gaining Ratio on Retirement/Death of a Partner

Options

(A)1 : 1

(B)1 : 2

(D)2 : 1

Official Answer

Correct option: (C) 4 : 1

Gaining Ratio = New Share − Old Share. $\text{Dharam gains } 11/20 - 7/20 = 4/20 \text{ and Karam gains } 9/20 - 8/20 = 1/20$ , giving a gaining ratio of 4 : 1.

gaining ratioretirement of a partnerdeath of a partnernew profit sharing ratioold profit sharing ratioreconstitution of partnershipsacrificing partner

Marking Scheme

11 mark for correctly selecting option (C) 4 : 1 with the gaining ratio computed as $\text{New Share} - \text{Old Share}$ for Dharam and Karam.
2If the OR alternative (death of Raju) is attempted instead, 1 mark for correctly selecting 1 : 1 as the new ratio between Deen and Hari.

Hint

$\text{Gaining Ratio} = \text{New Share} - \text{Old Share}$ for each continuing partner; do not confuse it with the new profit-sharing ratio itself.

Quick Oral Answer

Gaining ratio is the ratio in which continuing partners acquire the outgoing partner's share of profit; it is found by subtracting each partner's old share from their new share.

Analysis & Explanation

Concept

When a partner retires or dies, the continuing partners usually gain a share of profit at the retiring/deceased partner's expense. The Gaining Ratio = New Profit Share − Old Profit Share for each continuing partner, and it is used to distribute the retiring/deceased partner's share of goodwill among the gainers.

Working (Part a)

Old ratio of Dharam : Karam : Raman = 7 : 8 : 5 (out of 20).

$\text{Dharam's old share} = 7/20; \text{new share} = 11/20 \to \text{gain} = 4/20$
$\text{Karam's old share} = 8/20; \text{new share} = 9/20 \to \text{gain} = 1/20$

$\text{Gaining ratio} = 4/20 : 1/20 =$ 4 : 1, so option (C) is correct.

Why the other options are wrong

(A) 1:1 would be true only if both partners gained equally, which is not the case here.
(B) 1:2 reverses the ratio incorrectly.
(D) 2:1 does not match the actual computed gain of 4:1.

OR part (b) — for reference

Deen, Raju and Hari share 7 : 6 : 7 (out of 20). Raju (6/20) dies and Deen and Hari take his share equally, i.e. 3/20 each.

$\text{Deen's new share} = 7/20 + 3/20 = 10/20$
$\text{Hari's new share} = 7/20 + 3/20 = 10/20$

$\text{New ratio Deen : Hari} =$ 1 : 1 (option A of the OR part).

Common Mistakes

1Confusing gaining ratio with the new profit-sharing ratio itself instead of computing New Share − Old Share.
2Forgetting to convert all shares to a common denominator before subtracting.
3Assuming the gain is shared equally without actually calculating each partner's individual gain.

Interesting Facts

Section 37 of the Indian Partnership Act, 1932 entitles an outgoing partner (or their estate) to interest at 6% p.a. on the amount due if it is not settled immediately, or to a share of subsequent profits attributable to the use of their capital — the same Act that underlies gaining-ratio adjustments.

Gaining ratio calculations became a fixture of CBSE Class 12 Accountancy board papers after the retirement/death chapter was substantially expanded in the NCERT syllabus, reflecting the real-world frequency of partner exits in Indian family-run partnership firms.

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Frequently Asked Questions

What is the formula for gaining ratio?

$\text{Gaining Ratio} = \text{New Profit Share} - \text{Old Profit Share}$ , calculated separately for each continuing partner. A positive value means the partner has gained; a negative value would mean a sacrifice.

Why is gaining ratio important on a partner's retirement or death?

It is the ratio in which the continuing partners bear the retiring/deceased partner's share of goodwill, since they are the ones who gain that share of future profits.