Aptitude Questions: Mensuration Set 15

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Welcome to Online Quantitative Aptitude section in AffairsCloud.com. Here we are creating question sample from Mensuration that are important for IBPS, SBI, RBI, SSC, LIC and other competitive exams. We have included some questions that are repeatedly asked in exams !!

1. A deer and a rabbit can complete a full round on a circular track in 9 minutes and 5 minutes respectively. P, Q, R and S are the four consecutive points on the circular track which are equidistant from each other. P is opposite to R and Q is opposite to S. After how many minutes will they meet together for the first time at the starting point, when both have started simultaneously from the same point in same direction?
   1.15 minutes
   2.25 minutes
   3.35 minutes
   4.45 minutes
   5.None of these
   
   Answer & Explanation

   Answer – 4.45 minutes
   Explanation :
   Time taken by a deer to complete one round = 9 minutes
   Time taken by a rabbit to complete one round = 5 minutes

   They meet together for the first time at the starting point = LCM of 9 and 5 = 45 minutes.

   
   
2. A deer and a rabbit can complete a full round on a circular track in 9 minutes and 5 minutes respectively. P, Q, R and S are the four consecutive points on the circular track which are equidistant from each other. P is opposite to R and Q is opposite to S. After how many minutes will they meet together for the first time, when both have started simultaneously from the same point in same direction(in min)?
   1. 15/4
   2. 45/4
   3. 35/4
   4. 25/4
   5.None of these
   
   Answer & Explanation

   Answer – 2. 45/4
   Explanation :
   Circumference of the track = LCM of 9 and 5 = 45 m.
   Ratio of time of deer and rabbit = 9 : 5
   Ratio of speed of deer and rabbit = 5 : 9
   Relative Speed = 4 m/min
   They meet together for the first time at the starting point = 45/4 min
   
   
3. A cylindrical cistern whose diameter is 14 cm is partly filled with water. If a rectangular block of iron 22 cm in length, 14 cm in breadth and 7 cm in thickness is wholly immersed in water, by how many centi metre will the water level rise?
   1. 10 cm
   2. 14 cm
   3. 12 cm
   4. 15 cm
   5. None of these
   
   Answer & Explanation

   Answer – 2. 14 cm
   Explanation :
   Volume of the block = 22 * 14 * 7
   Radius of the cistern = 14/2 = 7
   Volume of the Cylinder = 22/7 * R²* h
   22/7 * R²* h = 22/7 * 7 * 7 * h
   22/7 * 7 * 7 * h = 22 * 14 * 7 => h = 14
   
   
4. A well with 28 m inside diameter is dug out 18 m deep. The earth taken out of it has been evenly spread all around it to a width of 21 m to form an embarkment. Find the height of the embarkment.
   1.3 m
   2.8 m
   3.9 m
   4.6 m
   5.None of these
   
   Answer & Explanation

   Answer – 1.3 m
   Explanation :
   22/7[(R²) – (r²)] * h = 22/7(7*7*18)
   [(35²) – (7²)]h = 14 * 14 * 18
   (42*28)h = 14*14*18
   h = 3 m
   
   
5. The radii of two cylinders are in the ratio 4:5 and their heights are in the ratio 5:7, What is the ratio of their curved surface areas?
   1. 2 : 5
   2. 4 : 7
   3. 4 : 7
   4. 2 : 3
   5.None of these
   
   Answer & Explanation

   Answer – 2. 4 : 7
   Explanation :
   2Πr1h1/2Πr2h2= [4/5 * 5/7] = 4:7
   
   
6. The ratio between the sides of a room is 3:2. The cost of white washing the ceiling of the room at 5 Rs per square metre is Rs. 2500 and the cost of papering the walls at Rs. 2 per square metre is Rs. 960.  The height of the room is? 
   1. 4.8 m
   2. 6.5 m
   3. 3.5 m
   4. 8.5 m
   5.None of these
   
   Answer & Explanation

   Answer – 1. 4.8 m
   Explanation :
   Area of Ceiling  = Total Cost / Cost of 1 sq. Unit
   = 2500/5 = 500
   l:b = 2x:3x
   l*b = 5x² = 500
   l = 30m & b = 20 m
   Area of the 4 wall = 960/2 = 480
   Height = 480 / 2(30 + 20) = 4.8m
   
   
7. A park is in the form of a square one of whose sides is 50 m. The area of the park excluding the circular lawn in the centre of the park is 1884 m². The radius of the circular lawn is ?
   1. 21 m
   2. 31 m
   3. 41 m
   4. 14 m
   5. None of these
   
   Answer & Explanation

   Answer – 4. 14 m
   Explanation :
   Area of park = 50 x 50 = 2500 m²
   Area of circular lawn = Area of park – area of park excluding circular lawn
   = 2500 – 1884
   = 616
   Area of circular lawn = (22/7) x r² = 616 m²
   ⇒ r² = (616 x 7) / 22
   = 28 x 7
   = 2 x 2 x 7 x 7
   ∴ r = 14 m
   
   
8. The perimeter of a rectangle and a square is 160 cm each. If the difference between their areas is 600 cm. Find the area of the rectangle.
   1.800 cm²
   2.500 cm²
   3.1000 cm²
   4.600 cm²
   5. None of these
   
   Answer & Explanation

   Answer – 3.1000 cm²
   Explanation :
   Perimeter of rectangle = Perimeter of Square = 160
   4a = 160 => a = 40
   Area of square = 1600
   1600 – lb = 600
   lb = 1000 cm²
   
   
9. The length of a plot is four times its breath. A playground measuring 400 square meters occupies one fourth of the total area of a plot. What is the length of the plot in meter.?
   1. 20
   2. 30
   3. 60
   4. 40
   5. 80
   
   Answer & Explanation

   Answer – 5. 80
   Explanation :
   Area of the plot = (4 x 400) m²
   = 1600 m²
   Breadth = y meter
   Length = 4y meter
   Now area = 4y x y = 1600 m²
   ⇒ y² = 400 m²
   ⇒ y = 20 m
   ∴ Length of plot = 4y =80 m
   
   
   
10. If the radius of the cone is doubled, keeping the height constant, what is the ratio of the volume of the smaller cone to larger cone?
    1.2:9
    2.5:7
    3.1:4
    4.1:7
    5.None of these
    
    Answer & Explanation

    Answer – 3.1:4
    Explanation :
    v1/v2 = (r1²) * h1 / (r2²) * h2 (h1=h2)
    (r)²/(2r)²
    v1/v2 = 1:4