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Do It Yourself · Q5

Q.Anu, Prabha and Milli are partners sharing profits equally. Anu retires. Calculate the future profit-sharing ratio of the continuing partners and the gaining ratio if they agree to acquire her share:

(a) in the ratio of 5 : 3;
(b) equally.
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New Share = Old Share + Gain, where Gain is the continuing partner's portion of the retiring partner's share.

  1. Splitting Anu's 1/3 in 5 : 3 gives Prabha and Milli new shares 13/24 and 11/24 (13 : 11), gaining 5 : 3.
  2. Splitting Anu's 1/3 equally keeps them at 1 : 1, gaining 1 : 1.

When the acquisition (gaining) ratio is stated, we first give the retiring partner's share to the continuing partners in that stated ratio — this portion is their gain — and then add it to their old share to find the new profit-sharing ratio.

As no old ratio is stated, the three partners shared profits equally, so each old share = 1/3. Anu's retiring share = 1/3.

(a) Anu's 1/3 is acquired in 5 : 3 (total 8 parts):

  • Prabha's gain = 1/3 × 5/8 = 5/24
  • Milli's gain = 1/3 × 3/8 = 3/24

New shares:

  • Prabha = 1/3 + 5/24 = 8/24 + 5/24 = 13/24
  • Milli = 1/3 + 3/24 = 8/24 + 3/24 = 11/24
PartnerOld ShareGainNew Share
Prabha1/35/2413/24
Milli1/33/2411/24

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