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GATE 2018 ME (ME1) – Question 4

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

A rectangle becomes a square after its length and breadth decrease by 10 m and 5 m respectively. It loses 650 m² of area. What was its original area?

  1. 1125 m²
  2. 2250 m²
  3. 2924 m²
  4. 4500 m²

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Correct answer: (B) 2250 m²

Explanation

Let the final square side be s. Original dimensions are s + 10 and s + 5. Lost area is $(s+10)(s+5)-s^2=15s+50=650$, giving s = 40 m. Original area is $50(45)=2250$ m² (B).