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SSC CGL 2025 PYQ — Question 65

SSC CGL - 18 Sep 2025 - Shift 3 • Quantitative Aptitude • Q65

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A statue that is 1.6 meters in height is positioned on top of a pedestal. From a location on the ground, the angle of elevation to the top of the statue measures 60°, while the angle of elevation to the top of the pedestal from the same point is 45°. Determine the height of the pedestal.

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Correct answer: C

Explanation

The correct answer is Option 3 i.e.  0.8(3+1)0.8(\sqrt3+ 1) m.

Let the height of the pedestal (BC) = x meters  

Total height = pedestal + statue = x + 1.6 meters (AC)

tan⁡60∘=ACCD=x+1.6CD\tan 60^\circ =\frac{AC}{CD}= \frac{x + 1.6}{CD}

⇒ 3=x+1.6CD\sqrt{3} = \frac{x + 1.6}{CD}

⇒ CD=x+1.63CD = \frac{x + 1.6}{\sqrt{3}}

tan⁡45∘=BCCD=xCD=1\tan 45^\circ = \frac{BC}{CD}=\frac{x}{CD} = 1

⇒ CD = x

x=x+1.63x = \frac{x + 1.6}{\sqrt{3}}

⇒ √3x = x + 1.6

⇒ √3x - x = 1.6

⇒ x(√3 - 1) = 1.6

⇒ x = 1.6/(√3 - 1)

⇒ x=1.6(3+1)(3−1)(3+1)=1.6(3+1)2=0.8(3+1)x = \frac{1.6(\sqrt{3} + 1)}{(\sqrt{3} - 1)(\sqrt{3} + 1)}= \frac{1.6(\sqrt{3} + 1)}{2}= 0.8(\sqrt{3} + 1) m