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 :

Q: 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**.

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

(D)7 : 8 : 5

Official Answer

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.

admission of a partnernew profit sharing ratiosacrifice ratioequal sacrificeold profit sharing ratioreconstitution of partnership

Marking Scheme

11 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.

Analysis & Explanation

Concept

When a new partner acquires their share equally from the existing partners, each old partner sacrifices the same fraction, regardless of their old profit-sharing ratio. The new share of each old partner = Old Share − Sacrifice.

Working

Old ratio: Chaman = 4/9, Vatika = 5/9
Mohan's share = 1/5, acquired equally, i.e. $\frac{1}{2} \times \frac{1}{5} = \frac{1}{10}$ from each old partner
Chaman's new share = $\frac{4}{9} - \frac{1}{10} = \frac{40-9}{90} = \frac{31}{90}$
Vatika's new share = $\frac{5}{9} - \frac{1}{10} = \frac{50-9}{90} = \frac{41}{90}$
Mohan's share = $\frac{1}{5} = \frac{18}{90}$

New ratio Chaman : Vatika : Mohan = 31 : 41 : 18, matching option (B).

Why other options are wrong

(A) 2:2:1 wrongly treats Chaman and Vatika as equal partners, ignoring their actual 4:5 old ratio.
(C) 41:31:18 swaps Chaman's and Vatika's shares.
(D) 7:8:5 does not reflect the correct sacrifice calculation at all.

Common Mistakes

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

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.

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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.