Step 1

Length of the ladder = $ 500$ cm

Let $ \theta$ be the angle between the floor and ladder.

$ \sin \theta = \large\frac{y}{500}$

On differentiating w.r.t $t$ we get,

$ \cos \theta \large\frac{d\theta}{dt}=\large\frac{1}{500} \times \large\frac{dy}{dt}$

It is given $ \large\frac{dy}{dt}=10\: cm/sec$

$ \cos \theta = \large\frac{x}{500}$ when $ x = 200$

$ \cos \theta = \large\frac{200}{500} = \large\frac{2}{5}$

Step 2

Substituting the respective values we get,

$ \large\frac{2}{5} \large\frac{d\theta}{dt} = \large\frac{1}{500} \times 10$

$ \Rightarrow \large\frac{ d\theta}{dt} = \large\frac{1}{50} \times \large\frac{5}{20}$

$ = \large\frac{1}{20} $ rad / sec

Hence the correct option is B