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:

The formula for Gaining Ratio is:
$$\text{Gaining Ratio}=\text{New Ratio}-\text{Old Ratio}$$
Old Ratio of Ranjana, Sadhna, and Kamana = $4:3:2$ Sadhna's Old Share = $\frac{3}{9}$ Kamana's Old Share = $\frac{2}{9}$ New Ratio of Sadhna and Kamana = $5:3$ Sadhna's New Share = $\frac{5}{8}$ Kamana's New Share = $\frac{3}{8}$ Sadhna's Gain:
$$\frac{5}{8}-\frac{3}{9}=\frac{45-24}{72}=\frac{21}{72}$$
Kamana's Gain:
$$\frac{3}{8}-\frac{2}{9}=\frac{27-16}{72}=\frac{11}{72}$$
Thus, the Gaining Ratio between Sadhna and Kamana is $21:11$.