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Numerical Questions · Q8

Q.A, B and C were partners in a firm sharing profits in 3:3:2 ratio. They admitted D as a new partner for 4/7 profit. D acquired his share 2/7 from A, 1/7 from B and 1/7 from C. Calculate new profit sharing ratio?

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After D's admission acquiring 4/7 from the old partners in specified fractions, the new profit-sharing ratio is A : B : C : D = 5 : 13 : 6 : 32.

Concept: Admission of a Partner and Reconstitution of Profit-Sharing Ratio

When a new partner is admitted and acquires his share from the existing partners in specified proportions, each old partner's share is reduced by the fraction he surrenders. The new ratio is calculated by subtracting the sacrifice from each old partner's original share.

The accounting treatment requires us to:

  1. Identify each old partner's original share
  2. Calculate the sacrifice made by each old partner (the portion of profit they give up to the new partner)
  3. Compute the new share for each old partner = Original share − Sacrifice
  4. The new partner's share is the sum of all sacrifices (or as stated in the problem)

The key principle: the total of all shares must always equal 1 (or the whole profit).

Solution

Working Note 1: Original Profit-Sharing Ratio of A, B and C

Given ratio = 3 : 3 : 2

Total parts = 3 + 3 + 2 = 8

  • A's original share = 3/8
  • B's original share = 3/8
  • C's original share = 2/8 = 1/4

Working Note 2: Sacrifice by Each Old Partner

D is admitted for 4/7 share of profit, which he acquires as follows:

  • From A: 2/7
  • From B: 1/7
  • From C: 1/7

Verification: 2/7 + 1/7 + 1/7 = 4/7 ✓

Therefore:

  • A's sacrifice = 2/7
  • B's sacrifice = 1/7
  • C's sacrifice = 1/7

Working Note 3: New Share of Each Partner

A's new share:

3/8 - 2/7

Taking LCM of 8 and 7 = 56:

(3 × 7)/56 - (2 × 8)/56 = (21 - 16)/56 = 5/56

B's new share:

3/8 - 1/7

21/56 - 8/56 = 13/56

C's new share:

2/8 - 1/7 = 1/4 - 1/7

Taking LCM of 4 and 7 = 28:

7/28 - 4/28 = 3/28

Converting to denominator 56: (3 × 2)/56 = 6/56

D's new share:

4/7 = (4 × 8)/56 = 32/56

Working Note 4: Verification and Final Ratio

Sum of all shares: …

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