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A and B are partners sharing profit in the ratio 3:2. C is admitted as a new partner. The new profit-sharing ratio among A, B, and C is 5:3:2. Calculate the sacrificing ratio.

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Final answer:

To find the sacrificing ratio, compare the old and new profit shares of the existing partners. For partners A and B, both are sacrificing 1/10 of the profits when the new partner C is admitted, resulting in a sacrificing ratio of 1:1.

Step-by-step explanation:

The question you are asking pertains to the calculation of the sacrificing ratio when a new partner is admitted into a business partnership. To calculate the sacrificing ratio, we identify how much of their original profit share each existing partner is giving up to the new partner. The original profit-sharing ratio between A and B is 3:2, which can also be written as A = 3/5 of profits and B = 2/5 of profits. The new profit-sharing ratio including C is 5:3:2. In order to find the sacrificing ratio, we compare the old and new ratios:

  • For A: Old share = 3/5, New share = 5/10 (or 1/2), so A sacrifices 3/5 - 1/2 = 1/10 of the profits.
  • For B: Old share = 2/5, New share = 3/10, so B sacrifices 2/5 - 3/10 = 1/10 of the profits.

Therefore, the sacrificing ratio of A to B is 1:1, indicating that A and B are sacrificing an equal portion of their profits to the new partner C.

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