Given below are three quantities named 1, 2 and 3. Based on the given information, you have to determine the relationship between the three quantities. You should use the given data and knowledge of Mathematics to choose between the possible answer. Quantity 1: Area of the innermost square. A square is made by joining the midpoints of a square of area 200 sq. m. The outermost square is called Square 1, The square inside it is called Square 2. The next square is made by joining midpoints of square 2 and is called Square 3. This process goes on. Square 5 is the innermost square. Quantity 2: A man starts with a speed of 10 km/hr. He increases his speed by 10 km/hr every hour at the start and drives at the same speed for that hour. If he traveled a total distance of 550 km. Find the time Quantity 3: Height of cylinder Its volume is equal to the volume of a cone whose radius is 14 cm and height is 39.3 cm. The radius of the cylinder is 14 cm Correct Answer Quantity 3 > Quantity 1 > Quantity 2 Quantity 1: Let the side of square 1 be a unit Area = a × a unit. Now, side of square formed by joining midpoints of square 1 will be half of diagonal of square (sides joining two midpoints of a triangle is parallel and half of third side) Side of square 2 = (Diagonal 1)/2 = √2 a/2 = a/√2 Area of square 2 = × = a2/2 Ratio = 2 : 1 Hence area will get divided by 2 every time, Area of square 5 = 200/24 = 12.5 m2 Quantity 2: Speed in 1st hour = 10 km/hr Distance in 1st hour = 10 km Speed in second hour = 20 km/hr Distance in second hour = 20 km Distance travelled will increase every hour in the same manner, Total distance = 10 + 20 + 30 + .... = 550 let time be Y hours /2 = 550/10 (sum of first n terms) Y (Y + 1) = 110 Y = 10 Quantity 3: Volume of cone = Volume of cylinder (π × r2 × h)/3 = π × R2 × H (39.3 × 142)/3 = (142 × H) 13.1 × 142 = 142 × H H = 13.1 cm Hence, Quantity 3 > Quantity 1 > Quantity 2