Multiple choice

(\text{In the following questions, two quantities are given as Quantity I and Quantity II. Find the correct relationship among them.}\\text{Quantity I:}\text{ Area of the square is 7200 cm}^2\text{ which is four times the area of the rectangle whose length and breadth is in the ratio of 9:8. What is the sum of length and breadth of the rectangle? }\\text{Quantity II:}\text{ A rectangular water tank is 300 cm} \times 488 \text{cm is dug inside a circular field. The area of the remaining portion is 12000cm}^2\text{ . Find the radius of the circular field.})

  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
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: Square area = 7200 = 4 × rectangle area, so rectangle area = 1800. Length:Breadth = 9:8, let dimensions be 9x and 8x. Then 72x² = 1800, x² = 25, x = 5. Length = 45, breadth = 40. Sum = 85. Quantity II: Tank area = 300 × 488 = 146400. Circular field area = 146400 + 12000 = 158400. πr² = 158400, r² = 158400/π ≈ 50414, r ≈ 224.5. Since 224.5 > 85, Quantity II > Quantity I.

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