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Illustrations · Illustration 2

Q.Alka, Harpreet and Shreya are partners sharing profits in the ratio of 3 : 2 : 1. Alka retires and her share is taken up by Harpreet and Shreya in the ratio of 3 : 2. Calculate the new profit sharing ratio.

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✓ Free question

New share = old share + acquired share. Harpreet ends at 19/30 and Shreya at 11/30, giving a new ratio of 19 : 11. (The gaining ratio is simply the agreed acquiring ratio, 3 : 2.)

Concept

When the retiring partner's share is taken by the continuing partners in a specified ratio, each continuing partner's new share is her own old share plus the portion of the retiring partner's share she acquires.

Solution

Old ratio Alka : Harpreet : Shreya = 3 : 2 : 1 (i.e. 3/6 : 2/6 : 1/6). Alka's share of 3/6 is acquired by Harpreet and Shreya in 3 : 2.

  • Harpreet acquires = 3/5 × 3/6 = 9/30; new share = 2/6 + 9/30 = 10/30 + 9/30 = 19/30
  • Shreya acquires = 2/5 × 3/6 = 6/30; new share = 1/6 + 6/30 = 5/30 + 6/30 = 11/30
✓Final answer

New profit sharing ratio of Harpreet and Shreya = 19 : 11; their gaining ratio is the agreed 3 : 2.

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