Multiple choice

Quantity I- the circumference of two circles is 88 meters and 132 meters respectively. What is the difference between the area of larger circle and smaller circle?\ Quantity II- A circle having the area of 616m2. If the circumference of this circle is equal to 200% of the length of the rectangle and width of the rectangle is equal to the perimeter of equilateral triangle with side 6m. What is the area of the rectangle

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established

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C Correct answer
Explanation

Quantity I: For circumferences 88 m and 132 m, radii are 44/π m and 66/π m. Areas are π × (44/π)² = 1936/π m² and π × (66/π)² = 4356/π m². Difference = (4356 - 1936)/π = 2420/π m². Using π = 22/7: Difference = 2420 × 7/22 = 770 m². Quantity II: Circle area 616 m² gives r = 14 m (using π = 22/7). Circumference = 88 m = 200% of rectangle length, so length = 44 m. Rectangle width = perimeter of triangle (side 6 m) = 18 m. Area = 44 × 18 = 792 m². Comparing: 792 > 770, so Quantity II > Quantity I.