Each question below contains a statement followed by Quantity I and Quantity
II. Compare the value derived from Quantity I and Quantity II and choose the correct option. Quantity I: The length of a rectangular field is 3 times its breadth. There is a square pond in it of area 108 square meters, which is one-fourth of the total area of the field. What is the breadth of the field? Quantity II: The ratio of length to breadth of a rectangle is 5 : 3. If the length of the rectangle is decreased by 8 m, it becomes a square. What is the side of the square thus formed?

Quantity I: Let the breadth of the rectangular field be B meters. Then, Length = 3B meters. Area of the field = Length × Breadth = 3B × B = 3B² sq. meters. ATQ, Area of pond = 1/4 × Area of field Or, 108 = 1/4 × 3B² Or, 3B² = 432 Or, B² = 144 So, B = 12 Hence, breadth of the field is 12 m. Quantity II: Let the length and breadth of the rectangle be 5x and 3x respectively. Since the rectangle becomes a square when length is decreased by 8 m, the new length must equal the breadth. ATQ, 5x - 8 = 3x Or, 2x = 8 Or, x = 4 So, side of the square = 3x = 3 × 4 = 12 m. Thus, Quantity I = 12 and Quantity II = 12. Therefore, Quantity I = Quantity II. Hence, the correct answer is E.