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Do It Yourself · Q4

Q.Azad, Vijay and Amit are partners sharing profits and losses in the proportion of 1/4, 1/8 and 10/16. Calculate the gaining ratio of the continuing partners in each of the following situations:

(a) Azad retires;
(b) Vijay retires;
(c) Amit retires.
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When a retiring partner's share is acquired in the old ratio, the gaining ratio of the continuing partners is the same as their old ratio.

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

The gaining ratio is Gain = New Share − Old Share for each continuing partner. There is a useful shortcut: when the retiring partner's share is distributed among the continuing partners in their old profit-sharing ratio, every continuing partner increases proportionately, so the gaining ratio comes out equal to the old ratio between those continuing partners. This is exactly the case here, since no separate acquisition ratio is given.

Express the old shares over 16: Azad = 4/16, Vijay = 2/16, Amit = 10/16, i.e. old ratio 2 : 1 : 5.

(a) Azad retires. Continuing partners Vijay and Amit gain in their old ratio 2/16 : 10/16 = 1 : 5. …

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