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CMA Intermediate · Financial Accounting · Admission of Partner

A and B share profits in the ratio 3:2. They admit C for a 1/5 share, which C takes 1/10 from A and 1/10 from B. What is the new profit-sharing ratio of A, B and C?

The new ratio is 5:3:2, written here as 25:15:10. A's share becomes 3/5 minus 1/10, which is 1/2; B's becomes 2/5 minus 1/10, which is 3/10; C holds 1/5. These sum to one whole, with A and B each sacrificing 1/10.

  1. A3:2:1
  2. B17:12:1
  3. C1:1:1
  4. D25:15:10Correct

Explanation

Old shares: A = 3/5 = 6/10, B = 2/5 = 4/10. A new share = 6/10 - 1/10 = 5/10 ... but 1/10 is a fraction of the whole firm, so A = 3/5 - 1/10 = 5/10, B = 2/5 - 1/10 = 3/10, C = 1/5 = 2/10. The ratio is 5:3:2, which equals 25:15:10 scaled by 5. Sacrifice by A and B is equal (1/10 each) and totals C's 1/5 share, which checks out.

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