Multiple choice

Directions: The question given below consists of a statement followed by Quantity I and Quantity II. Find the relationship between the quantities and choose the answer accordingly. The length of a rectangle is 6 cm more than its width and the area of the same rectangle is 60 cm more than 5 times its perimeter. Quantity I: If the breadth of the rectangular is increased by 5 cm and the length of the rectangle is decreased by 1 cm, what could be the area of the shape formed? Quantity II: If the breadth of the rectangle is increased by 4 cm, what could be the area of the rectangle?

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or relationship cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let width be w, length be w+6. Area = w(w+6) = w^2 + 6w. Perimeter = 2(2w+6) = 4w+12. Given w^2 + 6w = 5(4w+12) + 60 => w^2 + 6w = 20w + 120. w^2 - 14w - 120 = 0 => (w-20)(w+6) = 0. So w=20, l=26. Quantity I: (20+5)(26-1) = 25*25 = 625. Quantity II: 26(20+4) = 26*24 = 624. 625 > 624.

Keep practicing — related questions