RRB NTPC - Problems on Areas : Aptitude Test

1.

A large field of 900 hectares is divided into two parts. The difference of the areas of the two parts is one-fifth of the average of the two areas. What is the area of the smaller part in hectares?

   A.) 395
   B.) 385
   C.) 415
   D.) 405

Answer: Option 'C'

Let the areas of the parts be x hectares and (900 - x) hectares. 
Difference of the areas of the two parts = x - (900 - x) = 2x - 900
one-fifth of the average of the two areas = 1/5[x+(900−x)]/2 
= 1/5 × (900/2) = 450/5 = 90 
Given that difference of the areas of the two parts = one-fifth of the average of the two areas
=> 2x - 900 = 90
=> 2x = 990 
⇒ x = 990/2 = 495
Hence, area of smaller part = (900 - x) = (900 – 495) = 405 hectares.

2.

The length of a room is 6 m and width is 4.75 m. What is the cost of paying the floor by slabs at the rate of Rs. 900 per sq. metre. 

   A.) Rs. 25660
   B.) Rs. 25560
   C.) Rs. 25650
   D.) Rs. 26550

Answer: Option 'C'

Area = 6 × 4.75 sq. metre.
Cost for 1 sq. metre. = Rs. 900
Hence total cost = 6 × 4.75 × 900 = 6 × 4275 = Rs. 25650

3.

A rectangle measures 8 Cm on length and its diagonal measures 17 Cm. What is the perimeter of the rectangle? 

   A.) 46 cm
   B.) 48 cm
   C.) 46 m
   D.) None of these

Answer: Option 'C'

Second side = √172-82 
= √289-64 
= 15 cm 
Perimeter = 2 (l+b) = 2(8+5) Cm = 2(23) = 46 Cm

4.

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

5.

Find the area of the sector whose are is making an angle of 90° at the center of a circle of radius 3.2 Cm. 

   A.) 46.32 Sq.cm
   B.) 54.32 Sq.cm
   C.) 56.22 Sq.cm
   D.) 56.32 Sq.Cm

Answer: Option 'D'

Area of the sector = 90/360 × πr2 
= 90/360 × 22/7 × 3.2 × 3.2 
= (11 × 10.24)/2 = 112.64/2 = 56.32 Sq.Cm

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