Verified Solution • 2025–26 Session moderate

QJEEM16Ma20ad: JEE Main 2016 Mathematics - Class 12 JEEM16Ma20ad Solution: A man is walking towards a vertical pillar in a straight path,…

A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 30o. After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is 60o. Then the time taken (in minutes) by him, from B to reach the pillar, is :

Multiple Choice Options

  • A 6
  • B 10
  • C 20
  • D 5

Step-by-Step Verified Solution

According to given information, we have the following figure

JEE Main 2016 (Offline) Mathematics - Height and Distance Question 3 English Explanation
Now, from △ACD\triangle A C D and △BCD\triangle B C D , we have

tan⁡30∘=hx+y\tan 30^{\circ}=\frac{h}{x+y}

and tan⁡60∘=hy\tan 60^{\circ}=\frac{h}{y}

⇒h=x+y3...(i)\Rightarrow h=\frac{x+y}{\sqrt{3}}\quad...(i)

and h=3y...(ii)h=\sqrt{3} y\quad...(ii)

From Eqs. (i) and (ii),

x+y3=3y⇒x+y=3y\frac{x+y}{\sqrt{3}}=\sqrt{3} y \Rightarrow x+y=3 y

⇒x−2y=0⇒y=x2\Rightarrow x-2 y=0 \Rightarrow y=\frac{x}{2}

∵\because Speed is uniform.

∴\therefore Distance yy will be cover in 5 min5 \mathrm{~min} .

∵\because Distance xx covered in 10 min10 \mathrm{~min} .

∴\therefore Distance x2\frac{x}{2} will be cover in 5 min5 \mathrm{~min} .

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