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Rana, Sana and Kamana are partners, sharing profits in the ratio 4:3:2. Rana retires; Sana and Kamana decided to share profits in the future in the ratio of 5:3. The Gaining Ratio of Sana and Kamana will be

Solution

✅ Correct Option: 1

Old Profit Sharing Ratio (Rana : Sana : Kamana) = 4:3:2

Sana's old share = 39\frac{3}{9} = 13\frac{1}{3}

Kamana's old share = 29\frac{2}{9}


After Rana's retirement:

New Profit Sharing Ratio (Sana : Kamana) = 5:3

Sana's new share = 58\frac{5}{8}

Kamana's new share = 38\frac{3}{8}


Gaining Ratio = New Share - Old Share

Sana's gain = 58−39\frac{5}{8} - \frac{3}{9} = 4572−2472\frac{45}{72} - \frac{24}{72} = 2172\frac{21}{72}

Kamana's gain = 38−29\frac{3}{8} - \frac{2}{9} = 2772−1672\frac{27}{72} - \frac{16}{72} = 1172\frac{11}{72}

Gaining Ratio of Sana and Kamana = 2172:1172\frac{21}{72} : \frac{11}{72} = 21:11

The gaining ratio represents how much additional profit share each continuing partner acquires from the retiring partner's share. Since Rana held 49\frac{4}{9} of profits, this entire share gets distributed between Sana and Kamana in the ratio 21:11.

Correct Option: 1

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