 Aptitude Questions: Mensuration Set 12

Hello Aspirants. Welcome to Online Quantitative Aptitude section in AffairsCloud.com. Here we are creating question sample from Mensuration that are important for all the competitive exams. We have included some questions that are repeatedly asked in exams !!

1. If the area of a square is equal to the area of that rectangle whose width is double of the one side of the square then the ratio of the length to the breadth of the rectangle will be?
A. 1 : 2
B. 1 : 4
C. 1 : 6
D. 1 : 8
E. None of the Above
Answer – B. 1 : 4
Explanation :
b = 2a
a = b/2
Area of square = b²/4 = Area of rectangle
l * b = b²/4 => l = b/4
l / b =(b/4)/b => 1:4

2. In a rectangle the ratio of the length and breadth is 3:2. If each of the length and breadth is increased by 3m their ratio becomes 10:7. The area of the original rectangle in m² is?
A. 384
B. 486
C. 346
D. 476
E. None of the Above
Explanation :
[3x + 3 / 2x + 3] = 10/ 7
x = 9
Area of the original rectangle = 3x * 2x = 6x²
Area of the original rectangle = 6 * 81 = 486m²

3. The perimeter of a rectangular field is 120 m and the difference between its two adjacent sides is 30 m. The sides of the square field whose area is equal to this rectangular field is?
A. 15√2
B. 12√2
C. 15√3
D. 12√3
E. None of the Above
Explanation :
Perimeter of rectangle = 2(l + b) = 120
l + b = 60m — (1)
l – b = 30m –(2)
From (1) and (2)
l = 45 m; b = 15m
Area of rectangle = 675m² = Area of Square
Side of a square = 15√3

4. If each side pair of opposite sides of a square is increased by 10m, the ratio of the length and breadth of the rectangular so formed becomes 5:3. The area of the old square is?
A. 290m²
B. 225m²
C. 230m²
D. 245m²
E. None of the Above
Explanation :
(x+10) / x = 5 / 3
3x + 30 = 5x
x = 15m; Area = 225m²

5. The area of the garden formed by two concentric circles with circumferences 44m and 176 m respectively is?
A. 2390m²
B. 2590m²
C. 2310m²
D. 2490m²
E. None of the Above
Explanation : 2πR1 = 176
R1 = 28m
2πR2 = 44
R2 = 7m
Area  of the garden = π(R1² – R2²) = 22/7(784 – 49) =2310m²

6. One of the adjacent sides of a rectangular courtyard is 5m and its diagonal measures 13 m long. What is the area of the courtyard?
A. 60m²
B. 40m²
C. 50m²
D. 30m²
E. None of the Above
Explanation :
Another side = √[(13)² – (5)²] = 12m
Area = 12 * 5 = 60m²

7. The length of a park is four times of its breadth. A playground whose area is 1600 m² covers 1/4th part of the park. The length of the park is?
A. 108 m
B. 140 m
C. 120 m
D. 160 m
E. 180 m
Explanation :
l = 4b
Area of the park  = 4 * 1600 = 6400m²
l * b = 6400
l * l/4 = 6400
l² = 6400 * 4; l = 80 * 2 = 160 m

8. Two roads each 10m wide has been made running perpendicularly to each other inside a rectangular field of dimension 90m X 50m. What is the cost of spreading pebbles over them at the rate of Rs.8 per m².?
A. 10400
B. 15400
C. 17500
D. 20600
E. None of the Above
Explanation : Area of Roads = (l + b – w) * w
Area of Roads = (90 + 50 – 10) * 10 = 1300m²
Cost = 1300 * 8 = 10400

9. The width of a rectangular piece of land is 1/3 rd of its length. If the perimeter of the piece of land is 320m its length is?
A. 140 m
B. 128 m
C. 120 m
D. 156 m
E. 124 m
Explanation :
length = l ; breadth = l/3
2(l + b) = 320
2(l + l/3) = 320
l = 320 * 3/8 = 120m

10. The perimeter of a square and a rectangle are equal. If the length of rectangle is 24m and breadth of the rectangle is 1/3 rd of its length, then the area of the square will be?
A. 216m²
B. 256m²
C. 324m²
D. 625m²
E. None of the Above