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Do It Yourself · Q3

Q.Azad, Vijay and Amit are partners sharing profits and losses in the proportion of 1/4, 1/8 and 10/16 respectively. Calculate the new profit-sharing ratio between the continuing partners if:

(a) Azad retires;
(b) Vijay retires;
(c) Amit retires.
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When the acquisition ratio is not stated, the retiring partner's share is taken by the continuing partners in their old ratio, so the new ratio is just the old ratio among the remaining partners.

  1. Vijay : Amit = 1 : 5
  2. Azad : Amit = 2 : 5
  3. Azad : Vijay = 2 : 1

If a problem does not say in what ratio the continuing partners acquire the retiring partner's share, the assumption is that they gain it in their old profit-sharing ratio. As a result, the new profit-sharing ratio of the continuing partners is simply their old shares taken together as a ratio.

First put the old shares over a common denominator of 16 so they are easy to compare:

  • Azad = 1/4 = 4/16
  • Vijay = 1/8 = 2/16
  • Amit = 10/16

So the old ratio is 4 : 2 : 10, i.e. 2 : 1 : 5 (dividing by 2).

  1. If Azad retires, the remaining partners are Vijay and Amit, whose old shares are 2/16 : 10/16 = 2 : 10 = 1 : 5.
  2. If Vijay retires, the remaining partners are Azad and Amit, whose old shares are 4/16 : 10/16 = 4 : 10 = 2 : 5.
  3. If Amit retires, the remaining partners are Azad and Vijay, whose old shares are 4/16 : 2/16 = 4 : 2 = 2 : 1.
    ✓Final answer

    New profit-sharing ratio:

    1. Vijay : Amit = 1 : 5
    2. Azad : Amit = 2 : 5
    3. Azad : Vijay = 2 : 1

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