Two vertical lamp-posts of equal height stand on either side of a road $50$ m wide. At a point $\text{P}$ on the road between them, the elevation of the tops of the lamp-posts are $60^{\circ}$ and $30^{\circ}$. Find the distance of $\text{P}$ from the lamp-post which makes angle of $60^{\circ}$.
- $25$ m
- $12.5$ m
- $16.5$ m
- $20.5$ m