RRB NTPC - Problems on Areas : Aptitude Test

1.

The area of the largest circle that can be drawn inside a square of side 28 Cm in length is:

   A.) 616 Cm3
   B.) 626 Cm2
   C.) 619 Cm2
   D.) 616 Cm2

Answer: Option 'D'

Radius of required circle = 14 Cm 
its area = 22/7 × 14 × 14 
44 × 14 = 616 Cm2

2.

The sides of a rectangle are in the ratio of 6 : 5 and its area is 1331 sq.m. Find the perimeter of rectangle.

   A.) 120 m
   B.) 121 cm
   C.) 121 m
   D.) None of these

Answer: Option 'C'

Let 6x and 5x be sides of the rectangle 
6x × 5x = 1331 
11x2 = 1331 
x2 = 1331/11 = 121 => x = 11 
Length = 6x = 6 × 11 = 66 
Breadth = 5x => 5 × 11 = 55 
Perimeter = 2 (l+b) => 2 (66+55) = 121 m

3.

A girl walking at the rate of 9 Km per hour crosses a square field diagonally in 12 seconds. The area of the field is: 

   A.) 460 sq.m
   B.) 600 sq.m
   C.) 510 sq.m
   D.) 450 sq.m

Answer: Option 'D'

Distance covered in (9×1000)/(3600) × 12 = 30 m 
Diagonal of squarre field = 30 m. 
area of square field = 302/2
= 900/2 = 450 Sq.m

4.

The area of a rectangle plot is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the plot? 

   A.) 20 metres
   B.) 25 metres
   C.) 27 metres
   D.) 18 metres

Answer: Option 'A'

Answer: Option 'A'
lb = 460 m2...(Equation 1)
Let the breadth = b
Then length, l = b × (100+15)/100 = 115b/100 ...(Equation 2)
From Equation 1 and Equation 2,
115b/100 × b = 460
b2 = 46000/115 = 400
⇒ b = √400 = 20 m

5.

The area of a square field is 4802 m2 the length of its diagonal is: 

   A.) 94 m
   B.) 96 m
   C.) 98 m
   D.) None of these

Answer: Option 'C'

Let the diagonal be d metres, 
Then 1/2 d2 = 4802 
d2 = 9604 
d = √9604 
d = 98 m