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Do It Yourself · Q2

Q.Anita, Jaya and Nisha are partners sharing profits and losses in the ratio of 1 : 1 : 1. Jaya retires from the firm. Anita and Nisha decide to share future profits in the ratio of 4 : 3. Calculate the gaining ratio.

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✓ Free question

When a partner retires and the remaining partners fix a new profit-sharing ratio, each continuing partner's gain is New Share − Old Share. For Anita and Nisha, this gives 5/21 and 2/21, so the gaining ratio is 5 : 2.

The gaining ratio shows the proportion in which the continuing partners acquire the retiring partner's share of profit. It is the additional share each of them picks up because the retiring partner has left. The rule is simple: for every continuing partner, Gain = New Share − Old Share. This gaining ratio matters because the retiring partner's share of goodwill is later compensated by the continuing partners in exactly this ratio.

Old ratio is 1 : 1 : 1, so each partner's old share = 1/3. After Jaya retires, Anita and Nisha share future profits in 4 : 3, so Anita's new share = 4/7 and Nisha's new share = 3/7.

Anita's gain = 4/7 − 1/3 = (12 − 7)/21 = 5/21.

Nisha's gain = 3/7 − 1/3 = (9 − 7)/21 = 2/21.

PartnerOld ShareNew ShareGain (New − Old)
Anita1/34/75/21
Nisha1/33/72/21

The gains 5/21 and 2/21 have the same denominator, so the gaining ratio is simply 5 : 2.

✓Final answer

Gaining ratio (Anita : Nisha) = 5 : 2.

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