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Ranjana, Sadhna and Kamana are partners, sharing profits in the ratio 4:3:2. Ranjana retires; Sadhna and Kamana decide to share profits in the future at the ratio of 5:3. Calculate the Gaining Ratio:

Solution

✅ Correct Option: 3

Old Profit Sharing Ratio (Ranjana : Sadhna : Kamana) = 4:3:2

New Profit Sharing Ratio (Sadhna : Kamana) = 5:3 (after Ranjana's retirement)


To find the Gaining Ratio, we calculate: Gain = New Share - Old Share for each continuing partner.

For Sadhna:

Old Share = 39\frac{3}{9} = 13\frac{1}{3}

New Share = 58\frac{5}{8}

Gain = 58−13\frac{5}{8} - \frac{1}{3} = 15−824\frac{15-8}{24} = 724\frac{7}{24}

For Kamana:

Old Share = 29\frac{2}{9}

New Share = 38\frac{3}{8}

Gain = 38−29\frac{3}{8} - \frac{2}{9} = 27−1672\frac{27-16}{72} = 1172\frac{11}{72}


Gaining Ratio = Sadhna's Gain : Kamana's Gain

= 724\frac{7}{24} : 1172\frac{11}{72}

= 724×72\frac{7}{24} \times 72 : 1172×72\frac{11}{72} \times 72

= 2121 : 1111

Gaining Ratio = 21:11

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