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GATE 2026 EC – Question 9

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

The city of Atlantis was crafted by the God of the seas, Poseidon. It was made of alternating concentric circular rings of land (shaded) and water (not shaded) as represented in the figure (not to scale). The radius of Inner Island was 2.5 stades. The water surrounding Inner Island was one stade wide (length AB). This was surrounded by two pairs of alternating rings of land and water. The first pair of land and water was two stades wide each (lengths BC and CD), and the outer pair is three stades wide each (lengths DE and EF). The ratio of the surface area of the land to that of the water in the city of Atlantis is ________ (round off to two decimal places).

Diagram for GATE 2026 EC question 9
  1. 0.45
  2. 0.60
  3. 0.75
  4. 0.90

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Show answer and explanation

Correct answer: (C) 0.75

Explanation

Boundary radii are 2.5, 3.5, 5.5, 7.5, 10.5, 13.5. Land area is $\pi(6.25+18+54)=78.25\pi$ and water area is $\pi(6+26+72)=104\pi$. The ratio is $78.25/104\approx0.75$.