UPSC CDS 1 2022 Math Paper

Given:
The angle of elevation of the top of a tower of height x meter from a point on the ground is found to be 60∘
By going y metre away from that point, it becomes 30∘
Concept used:
tan‌θ=P∕B
Here P= perpendicular, B= base According to the question,
tan‌60∘=AB∕BC
⇒√3=x∕BC
⇒BC=x∕√3
‌ Again, ‌tan‌30∘=AB∕BD
⇒1∕√3=AB∕BD
⇒1∕√3=x∕BD
⇒BD=√3x
BD=BC+CD
⇒√3x=x∕√3+y‌‌‌ [From equation (1) ‌
⇒√3x=(x+√3y)∕√3
⇒3x=x+√3y
⇒2x=√3y
∴ Required answer is Option 3