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SSC CGL 2023 PYQ — Question 19

SSC CGL Tier II - 26 October 2023 • Quantitative Aptitude • Q19

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Two pillars of equal height stand on either side of a roadway which is 150 m wide. At a point in the road between pillars, the elevations of the pillars are xo and yo that tan⁡x∘=25,tan⁡y∘=35\tan x^\circ = \frac{2}{5}, \tan y^\circ = \frac{3}{5}, then the height of each pillar is:

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 36 m.

As seen in the figure

Tan x = 25\frac{2}{5}  and tan y =35\frac{3}{5}

Since tan A = Perpendicular/base

Hence, h150−a\frac{h}{150 - a} = 25\frac{2}{5} and ha\frac{h}{a} = 35\frac{3}{5}

Equating h in both equations we get

⇒ 25\frac{2}{5}(150 - a) = 35\frac{3}{5}a

Hence we get the value of a

 ⇒ a = 60

Now since ha\frac{h}{a} = 35\frac{3}{5}, we get h = 36

Hence, the height of each pillar is 36 m.