The ratio of present ages of Ratnabali and Shaukat is $8:5$. After 22 years the ratio of their ages will be $10:9$. At present, what is Ratnabali's age?

Let the present ages of Ratnabali and Shaukat be $8x$ and $5x$ respectively.After 22 years, their ages will be $8x+22$ and $5x+22$.According to the problem:
$$\frac{8x+22}{5x+22}=\frac{10}{9}$$
Cross-multiply to solve for $x$:
$$9(8x+22)=10(5x+22)$$
$$72x+198=50x+220$$
$$72x-50x=220-198$$
$$22x=22$$
$$x=1$$
Now, calculate Ratnabali's present age:
$$\text{Ratnabali’s age}=8x=8\times 1=8\text{ years}$$