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Q.A, B and C were partners in a firm sharing profits and losses in the ratio of 5 : 3 : 2. D was admitted as a new partner for 1/5th share in the profits of the firm. D acquired his share entirely from A. The new profit sharing ratio between A, B, C and D will be : (A) 5 : 2 : 2 : 1 (B) 3 : 3 : 2 : 2 (C) 3 : 2 : 3 : 2 (D) 4 : 3 : 2 : 1

CBSECBSE Class XII Board 2025MCQ· 1mImportance★★★★★
✓ Free question

D acquires his 15\frac{1}{5} share entirely from A, so only A's share is reduced. The new profit sharing ratio is 3 : 3 : 2 : 2 (option B).

Concept: Admission of a Partner and Sacrifice of Share

When a new partner is admitted, the existing partners sacrifice a portion of their profit share in favour of the incoming partner. The sacrificing ratio determines how much each old partner gives up.

In this problem, D acquires his share entirely from A. This is a specific case where:

  • Only A sacrifices; B and C retain their original shares unchanged.
  • A's new share = A's old share − D's share.

The accounting treatment requires us to first establish the old shares, then compute the sacrifice, and finally determine the new profit sharing ratio for all four partners.

Understanding the Old Profit Sharing Ratio

The old ratio among A, B and C is 5 : 3 : 2.

Total parts = 5+3+2=105 + 3 + 2 = 10

So:

  • A's share = 510=12\frac{5}{10} = \frac{1}{2}
  • B's share = 310\frac{3}{10}
  • C's share = 210=15\frac{2}{10} = \frac{1}{5}

D's Admission and the Sacrifice

D is admitted for 15\frac{1}{5} share in the profits of the firm, and he acquires this share entirely from A.

This means:

  • A sacrifices = 15\frac{1}{5} (the entire share given to D)
  • B sacrifices = 00 (B retains his original share)
  • C sacrifices = 00 (C retains his original share)

Calculating the New Profit Sharing Ratio

A's new share:

Anew=Aold−Sacrifice=12−15A_{\text{new}} = A_{\text{old}} - \text{Sacrifice} = \frac{1}{2} - \frac{1}{5}

To subtract, find a common denominator (10):

Anew=510−210=310A_{\text{new}} = \frac{5}{10} - \frac{2}{10} = \frac{3}{10}

B's new share:

B retains his original share (no sacrifice):

Bnew=310B_{\text{new}} = \frac{3}{10}

C's new share:

C retains his original share (no sacrifice):

Cnew=210=15C_{\text{new}} = \frac{2}{10} = \frac{1}{5}

D's share:

D=15=210D = \frac{1}{5} = \frac{2}{10}

Expressing the New Ratio

The new shares are:

  • A : B : C : D = 310:310:210:210\frac{3}{10} : \frac{3}{10} : \frac{2}{10} : \frac{2}{10}

Multiply through by 10 to clear denominators:

A:B:C:D=3:3:2:2A : B : C : D = 3 : 3 : 2 : 2

Tip

When a new partner acquires share from only one old partner, that partner's share is reduced by the exact amount given to the new partner, while all other partners' shares remain unchanged.

Watch out

A common mistake is to assume that all old partners sacrifice equally or in their old ratio. Always read carefully: here, D acquires entirely from A, so only A sacrifices.

Working Note 1: Verification of Total Shares

New ratio sum = 3+3+2+2=103 + 3 + 2 + 2 = 10 parts, which equals the original 10 parts. ✓

Alternatively, in fractional form:

310+310+210+210=1010=1\frac{3}{10} + \frac{3}{10} + \frac{2}{10} + \frac{2}{10} = \frac{10}{10} = 1 ✓

✓Final answer

The new profit sharing ratio between A, B, C and D is 3 : 3 : 2 : 2. The correct answer is (B).

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