Multiple choice

X and Y are partners in a business sharing profits and losses in the ratio of 3 : 2. They admit Z as a new partner with 1/5 share in the profits. Calculate the new profit sharing ratio of the partners.

  1. 12 : 8 : 5

  2. 12 : 8 : 6

  3. 12 : 7 : 6

  4. 12 : 3 : 7
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A Correct answer
Explanation

Remaining share after Z gets 1/5 is 4/5. This is divided between X and Y in 3:2 ratio. X's new share = 3/5 * 4/5 = 12/25. Y's new share = 2/5 * 4/5 = 8/25. Z's share = 1/5 = 5/25. Ratio is 12:8:5.

AI explanation

Let the total profit be 1, so the new partner Z receives a 1/5 share, leaving a combined profit share of 4/5 for X and Y. The old profit sharing ratio of 3 to 2 means X gets 3/5 of the remaining profit and Y gets 2/5 of the remaining profit. Therefore, X's new ratio is 3/5 * 4/5 = 12/25, Y's new ratio is 2/5 * 4/5 = 8/25, and Z's ratio is 1/5 = 5/25. The new profit sharing ratio of X, Y, and Z is 12 : 8 : 5.

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