The median of $$100$$ observations grouped in classes of equal width is $$25$$. If the median class interval is $$20-30$$ and the number of observations less than $$20$$ is $$45$$, then the frequency of median class is

Total number of observations $$n = 100$$. Therefore the median is the $$\left(\dfrac{n}{2}\right)^{\text{th}} = 50^{\text{th}}$$ observation.

The median class is given as $$20-30$$, so

lower boundary of the class $$l = 20$$,
class width $$h = 30-20 = 10$$.

For a continuous grouped distribution the median is computed by
$$\text{Median} = l + \dfrac{\dfrac{n}{2} - c_f}{f}\,h \quad -(1)$$
where

$$c_f$$ = cumulative frequency of all classes preceding the median class,
$$f$$ = frequency of the median class.

It is given that the number of observations that are <20 is $$45$$. Hence $$c_f = 45$$.

Substituting all known values in equation $$-(1)$$:

$$25 = 20 + \dfrac{50 - 45}{f}\,(10)$$

$$25 = 20 + \dfrac{5}{f}\,(10)$$

$$25 = 20 + \dfrac{50}{f}$$

$$5 = \dfrac{50}{f}$$

$$f = 10$$.

Hence, the frequency of the median class is $$10$$.

Option A which is: $$10$$