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

The formula to calculate Gaining Ratio is:
$$\text{Gaining Ratio}=\text{New Share}-\text{Old Share}$$
Given data:Old Ratio of Rana, Sana, and Kamana = $4:3:2$ Old share of Sana = $\frac{3}{9}$ Old share of Kamana = $\frac{2}{9}$ New Ratio of Sana and Kamana = $5:3$ New share of Sana = $\frac{5}{8}$ New share of Kamana = $\frac{3}{8}$ Now, calculate the gain for each remaining partner:For Sana:
$$\text{Gain}=\frac{5}{8}-\frac{3}{9}=\frac{45-24}{72}=\frac{21}{72}$$
For Kamana:
$$\text{Gain}=\frac{3}{8}-\frac{2}{9}=\frac{27-16}{72}=\frac{11}{72}$$
Comparing their individual gains, we get the structural ratio:
$$\text{Gaining Ratio}=21:11$$