Aptitude Questions – Mensuration Set 16

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. In a rectangle the ratio of the length and breadth is 3:2. If each of the length and breadth is increased by 4m their ratio becomes 10:7. The area of the original rectangle in m² is?
   A. 846
   B. 864
   C. 840
   D. 876
   E. None of the Above
   
   Answer & Explanation

   Answer – B. 864m²
   Explanation :
   [3x + 4 / 2x + 4] = 10/7
   x = 12
   Area of the original rectangle = 3x * 2x = 6x²
   Area of the original rectangle = 6 * 144 = 864m²
   
   
2. The perimeter of a rectangle and a square is 160 cm each. If the difference between their areas is 500 cm. If the area of the rectangle is less than that of a Square then find the area of the rectangle?
   A. 1800 cm²
   B. 1500 cm²
   C. 1100 cm²
   D. 1600 cm²
   5. None of these
   
   Answer & Explanation

   Answer – C.1100 cm²
   Explanation :
   Perimeter of rectangle = Perimeter of Square = 160
   4a = 160 => a = 40
   Area of square = 1600
   1600 – lb = 500
   lb = 1100 cm²
   
   
3. Circumference of a circle A is 22/7 times perimeter of a square. Area of the square is 441 cm². What is the area of another circle B whose diameter is half the radius of the circle A(in cm²)?
   A. 354.5
   B. 346.5
   C. 316.5
   D. 312.5
   E. None of the Above
   
   Answer & Explanation

   Answer – B. 346.5
   Explanation :
   Area = 441 cm²
   a = 21 cm
   Perimeter of Square = 4 * 21
   Circumference of a Circle = 4 * 21 * 22/7
   2πr = 4 * 3 * 22
   r = 12 * 22 * 7 / 2 * 22 = 42 cm
   Radius of Circle B = 42/4 = 10.5 cm
   Area of Circle = πr² = 22/7 * 10.5 * 10.5 = 346.5 cm²
   
   
4. The area of a rectangle is equal to the area of a square whose diagonal is 12√2 metre. The difference between the length and the breadth of the rectangle is 7 metre. What is the perimeter of rectangle ? (in metre).
   A. 68 metre
   B. 50 metre
   C. 62 metre
   D. 64 metre
   E. None of the Above
   
   Answer & Explanation

   Answer – B. 50 metre
   Explanation :
   d = a√2
   12√2 = a√2
   a = 12
   l * b = a² = (12²) = 144
   l – b = 7 ; l = b + 7
   (b + 7)*(b) = 144
   b² + 7b – 144 = 0
   b = 9; l = 16
   2(l + b) = 2(16 + 9) = 50m
   
   
5. The area of a rectangle gets reduced by 9 square units,if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and breadth by 2 units, then the area is increased by 67 square units. Find the area of the rectangle?
   A. 159 m
   B. 179 m
   C. 147 m
   D. 153 m
   E. None of the Above
   
   Answer & Explanation

   Answer – D. 153 m
   Explanation :
   Length = x; Breadth =y
   xy – (x-5)(y+3) = 9
   3x – 5y – 6 = 0 —(i)
   (x+3)(y+2) – xy = 67
   2x + 3y -61 = 0 —(ii)
   solving (i) and (ii)
   x = 17m ; y = 9m
   Area of the Rectangle = 153 m
   
   
6. The length of a plot is four times its breath. A playground measuring 900 square meters occupies one fourth of the total area of a plot. What is the length of the plot in meter.?
   A. 150
   B. 130
   C. 160
   D. 140
   E. 120
   
   Answer & Explanation

   Answer – E. 120
   Explanation :
   Area of the plot = (4 x 900) m²
   = 3600 m²
   Breadth = y meter
   Length = 4y meter
   Now area = 4y x y = 3600 m²
   ⇒ y² = 900 m²
   ⇒ y = 30 m
   ∴ Length of plot = 4y =120 m
   
   
7. The sum of the radius and height of a cylinder is 19m. The total surface area of the cylinder is 1672 m², what is the radius and height of the cylinder?(in m)
   A. 12, 7
   B. 11, 8
   C. 13, 6
   D. 14, 5
   E. 10, 9
   
   Answer & Explanation

   Answer – D. 14, 5
   Explanation :
   r + h = 19 m
   2πr(r + h) = 1672
   r = 1672 * 7/ 2 * 22 * 19 = 14
   r = 14 ; h = 5
   
   
8. If each side pair of opposite sides of a square is increased by 20 m, the ratio of the length and breadth of the rectangular so formed becomes 5:3. The area of the old square is?
   A. 990m²
   B. 900m²
   C. 930m²
   D. 945m²
   E. None of the Above
   
   Answer & Explanation

   Answer – B. 900m²
   Explanation :
   (x+20) / x = 5 / 3
   3x + 60 = 5x
   x = 30m; Area = 900m²
   
   
9. The length of a park is four times of its breadth. A playground whose area is 1024 m² covers 1/4th part of the park. The length of the park is?
   A. 118 m
   B. 142 m
   C. 124 m
   D. 126 m
   E. 128 m
   
   Answer & Explanation

   Answer – E. 128 m
   Explanation :
   l = 4b
   Area of the park  = 4 * 1024 m²
   l * b = 4 * 1024
   l * l/4 = 4 * 4 * 1024
   l² = 1024 * 16; l = 32 * 4 = 128 m
   
   
10. The width of a rectangular piece of land is 1/4 th 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
    
    Answer & Explanation

    Answer – B. 128 m
    Explanation :
    length = l ; breadth = l/4
    2(l + b) = 320
    2(l + l/4) = 320
    l = 320 * 4/10 = 128m