Quant Quiz “mensuraton” for SSC CGL 2016

Q1. If the length and the perimeter of a rectangle are in the ratio 5:16. Then its length and breadth will be in the ratio   
(a) 5:11
(b) 5:8
(c) 5:4
(d) 5:3
S1. Ans.(d)
Sol. Let length = 5x
⇒ breadth =(16x – 2 × 5x)/2=3x
∴ Required ratio =5x/3x
= 5: 3

Q2. ABC is a right angled triangle, B being the right angle. Mid-points of BC and AC are respectively B’ and A’. The ratio of the area of the quadrilateral AA’B’B of the area of the triangle ABC is 
(a) 1: 2
(b) 2: 3
(c) 3: 4
(d) None of the above

Q3. If the arcs of unit length in two circles subtend angles of 60° and 75° at their centres, the ratio of their radii is
(a) 3: 4
(b) 4: 5
(c) 5: 4
(d) 3: 5
S3. Ans.(c)
Sol. By using result,
R1 θ1=R2 θ2
R1/R2 =θ2/θ1 =(75°)/(60°)=5/4=5:4

Q4. If the altitude of a triangle is increased by 10% while its area remains same, its corresponding base will have to be decreased by 
(a) 10%
(b) 9%
(c) 100/11%
(d) 100/9%

Q5. A cuboidal water tank has 216 liters of water. Its depth is 1/3 of its length and breadth is 1/2 of 1/3 of the difference of length and height. The length of the tank is  
(a) 72 dm
(b) 18 dm
(c) 6 dm
(d) 2 dm
S5. Ans.(b)
Sol. Let l=9x,   h=3x,   b=x
l×b×h=216×1000
(1 litre = 1000 cm3)
9x×3x×x=216000
27x^3=216000
x^3=8000
x=20
l=180 cm = 18 dm

Q6. A wooden box measures 20 cm by 12 cm by 10 cm. Thickness of wood is 1 cm. Volume of wood to make the box (in cube cm) is
(a) 960
(b) 519
(c) 2400
(d) 1120
S6. Ans.(a) 
Sol. 
The external dimensions of the box are
l = 20 cm,     b = 12 cm,     h = 10 cm
External volume of the box = 20 × 12 × 10 = 2400 cm3
Thickness of the wood = 1 cm
Internal length = 20 – 2 = 18 cm
Internal breadth = 12 – 2 = 10 cm
Internal height = 10 – 2 = 8 cm
Internal volume of the box = 18 × 10 × 8 = 1440 cm3
Volume of the wood = (2400 – 1440) cm3
= 960 cm3

Q7. The area of three adjacent faces of a cuboid are x, y, z square units respectively. If the volume of the cuboid by v cube units, then the correct relation between v, x, y, z is  

Q8. The area of three consecutive faces of a cuboid are 12 cm2, then the volume (in cm3) of the cuboid is 
(a) 3600
(b) 100
(c) 80
(d) 24 √3
S8. Ans.(d)
Sol. Let the three sides of the cuboid be l, b and h
⇒ lb = bh = hl = 12
⇒ l^(2  ) b^2 h^2=12×12×12=1728
⇒lbh=√1728=12√12
=24√3  cm^3

Q9. Three solid iron cubes of edges 4 cm, 5cm and 6 cm are melted together to make a new cube, 62cm3 of the melted material is lost due to improper handing. The area (in cm2) of the whole surface of the newly formed cube is 
(a) 294
(b) 343
(c) 125
(d) 216

Q10. A low land, 48 m long and 31.5 m broad is raised to 6.5 dm. For this, earth is removed from a cuboidal hole, 27 m long and 18.2 m broad, dug by the side of the land. The depth of the hole will be.
(a) 3 m
(b) 2 m
(c) 2.2 m
(d) 2.5 m
S10. Ans.(b) 
Sol. According to the question                                            
 Let depth of the hole = d
∴ 48 m×31.5×6.5/10 m
=27×18.2×d               ( 1 dm =1/10 m )
 d = 2m      





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