Chaman and Vatika were partners in a firm sharing profits and losses in the ratio of 4 : 5. They admitted Mohan as a new partner for $\frac{1}{5}$th share in the profits of the firm. Mohan acquired his share equally from Chaman and Vatika. The new profit sharing ratio of Chaman, Vatika and Mohan will be :

**Correct option: (B) 31 : 41 : 18** Mohan acquires 1/5 equally from Chaman and Vatika, i.e., 1/10 from each. Chaman's new share = $\frac{4}{9} - \frac{1}{10} = \frac{31}{90}$; Vatika's new share = $\frac{5}{9} - \frac{1}{10} = \frac{41}{90}$; Mohan's share = $\frac{1}{5} = \frac{18}{90}$. New ratio (Chaman : Vatika : Mohan) = **31 : 41 : 18**.

Question 151 markMCQSection A

$\frac{1}{5}$

Reconstitution of a Partnership Firm: Admission of a Partner

New Profit Sharing Ratio on Admission of a Partner

Options

(A)

2 : 2 : 1

(B)

31 : 41 : 18

(C)

41 : 31 : 18

(D)

7 : 8 : 5

Official answer

\frac{4}{9} - \frac{1}{10} = \frac{31}{90}

admission of a partner

new profit sharing ratio

sacrifice ratio

equal sacrifice

old profit sharing ratio

reconstitution of partnership

Marking scheme

1. $1 mark for correctly computing Mohan's equal sacrifice of 1/10 from each partner and arriving at the new ratio 31:41:18 (option B).$

Hint

$Equal sacrifice means each old partner gives up the SAME fraction of the new partner's share, not the same proportion of their own share — subtract this equal fraction from each partner's old share.$

Quick oral answer

$When a new partner acquires their share equally from existing partners, each old partner gives up the same fixed fraction — here 1/10 each — which is then subtracted from their old share to get the new ratio of 31:41:18.$

Common mistakes

1. $Assuming 'acquired equally' means the new partner's share reduces both old partners' ratio proportionally rather than by an equal absolute fraction.$
2. $Adding the sacrifice to the old partners' shares instead of subtracting it.$
3. $Making an arithmetic slip while converting fractions to a common denominator of 90.$

Analysis and explanation

\frac{1}{2} \times \frac{1}{5} = \frac{1}{10}

Interesting facts

$The 'equal sacrifice' clause is one of the most common variations tested in CBSE admission-of-partner numericals precisely because it is easy to confuse with 'sacrifice in the old ratio', which follows a completely different formula.$

$Most real Indian partnership deeds specify sacrifice 'in the old ratio' by default; an explicit 'equally' clause, as in this question, must always override that default.$

Question details

Q15 of 39 questions

Board: CBSE
Class: Class 12
Subject: Accountancy
Year: 2026
Section: Section A
Marks: 1
Type: MCQ
Chapter: Reconstitution of a Partnership Firm: Admission of a Partner
Topic: $New Profit Sharing Ratio on Admission of a Partner$
Bloom's level: apply
Syllabus topic: $Unit 1: Accounting for Partnership Firms — Reconstitution: Admission of a Partner — New Profit Sharing Ratio$
Author: CBSE
Reviewed by: Padhantu Academic Team

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Frequently asked questions

$What does it mean when a new partner acquires their share 'equally' from existing partners?$

$It means each existing partner gives up the same absolute fraction of the total profits (here 1/10 each) to make up the new partner's share, regardless of the old partners' original profit-sharing ratio.$

$How is the new partner's share converted into a common fraction with the old partners?$

$All shares are expressed with a common denominator (here 90) so that Chaman's, Vatika's, and Mohan's shares can be compared and combined into a single new ratio.$