Present ages of Neha and Rashmi are in the ratio of $7:8$ respectively. Six years hence, the ratio of their ages will become $9:10$ respectively. What is Rashmi's present age?

Let the present ages of Neha and Rashmi be $7x$ and $8x$ years respectively.
Six years later, their ages will be $(7x+6)$ and $(8x+6)$ years.

According to the problem:

$$\frac{7x+6}{8x+6}=\frac{9}{10}$$

Cross-multiplying gives:

$$10(7x+6)=9(8x+6)$$

$$70x+60=72x+54$$

$$60-54=72x-70x$$

$$2x=6⟹x=3$$

Rashmi's present age $=8x=8\times 3=24$ years.