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GATE 2018 EC – Question 5

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

A 1.5 m tall person is standing at a distance of 3 m from a lamp post. The light from the lamp at the top of the post casts her shadow. The length of the shadow is twice her height. What is the height of the lamp post in meters?

  1. 1.5
  2. 3
  3. 4.5
  4. 6

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Show answer and explanation

Correct answer: (B) 3

Explanation

The shadow is $2\times1.5=3$ m long. The lamp post and the person form similar triangles: the lamp's height $H$ and the person's height 1.5 m relate as $\frac{H}{3+3}=\frac{1.5}{3}$, so $H=3$ m.