Quantitative Aptitude

General Questions

Quantitative Aptitude Exercise Mode

General Questions

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Question 1

The perimeter of one face of a cube is 20 cm. Its volume must be :

A
125 cm³
B
400 cm³
C
1000 cm³
D
8000 cm³
Correct Answer: Option A

Correct Answer: A. 125 cm³ ✅

  • A. 125 cm³ ✅ — Correct.
  • B. 400 cm³ ❌
  • C. 1000 cm³ ❌
  • D. 8000 cm³ ❌

Explanation:
A face of a cube is a square.

Perimeter of one face = 20 cm.
Side of the square = 20 ÷ 4 = 5 cm.

Volume of cube = side³
= 5³
= 125 cm³.

Exam Fact:
For a cube, Volume = side³. The perimeter of one face is 4 × side.

Therefore, the correct answer is A. 125 cm³ ✅.

Question 2

A rectangular water tank is 80 m × 40 m. Water flows into it though a pipe 40 Sq. cm at the opening at a speed of 10 Km/Hr. By how much, the water level will rise in the tank in half an hour ?

A
3/2 cm
B
4/9 cm
C
5/8 cm
D
None of these
Correct Answer: Option C

Correct Answer: C. 5/8 cm ✅

  • A. 3/2 cm ❌
  • B. 4/9 cm ❌
  • C. 5/8 cm ✅ — Correct.
  • D. None of these ❌

Explanation:
Dimensions of the tank = 80 m × 40 m.
Area of tank base = 80 × 40 = 3200 m².

Area of pipe opening = 40 cm² = 40/10,000 = 0.004 m².
Speed of water = 10 km/hr = 10,000 m/hr.

Volume of water flowing in 1 hour:
= 0.004 × 10,000 = 40 m³.

In half an hour:
Volume = 40 × 1/2 = 20 m³.

Let the rise in water level be h metres.
Volume = Area of tank × height
20 = 3200 × h
h = 20/3200 = 0.00625 m.

Converting to centimetres:
0.00625 × 100 = 0.625 cm = 5/8 cm.

Exam Fact:
For water tanks, use Volume = Base Area × Rise in Water Level. Also remember to convert all units to the same system before calculating.

Therefore, the correct answer is C. 5/8 cm ✅.

Question 3

50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m³, then the rise in the water lavel in the tank will be:

A
20 cm
B
25 cm
C
35 cm
D
50 cm
Correct Answer: Option B

Correct Answer: B. 25 cm ✅

  • A. 20 cm ❌
  • B. 25 cm ✅ — Correct.
  • C. 35 cm ❌
  • D. 50 cm ❌

Explanation:
Number of men = 50.
Displacement by each man = 4 m³.

Total volume of displaced water = 50 × 4 = 200 m³.

Base area of the tank = 40 × 20 = 800 m².

Let the rise in water level be h metres.
Volume displaced = Base area × Rise
200 = 800 × h
h = 200/800 = 0.25 m.

Converting into centimetres:
0.25 × 100 = 25 cm.

Exam Fact:
Rise in water level = Volume displaced ÷ Base area of tank.

Therefore, the correct answer is B. 25 cm ✅.

Question 4
A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:

A
720
B
900
C
1200
D
1800
Correct Answer: Option C

2(15 + 12) x h = 2(15 x 12)

h = 180 m = 20 m.
27 3

Volume = 15 x 12 x 20 m3 = 1200 m3.
3

Question 5
A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm3, then the weight of the pipe is:

A
3.6 kg
B
3.696 kg
C
36 kg
D
36.9 kg
Correct Answer: Option B

External radius = 4 cm,

Internal radius = 3 cm.

Volume of iron
= 22 x [(4)2 - (3)2] x 21 cm3
7
= 22 x 7 x 1 x 21 cm3
7
= 462 cm3.

Weight of iron = (462 x 8) gm = 3696 gm = 3.696 kg.

Question 6
A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:

A
4830
B
5120
C
6420
D
8960
Correct Answer: Option B

Clearly, l = (48 - 16)m = 32 m,

b = (36 -16)m = 20 m,

h = 8 m.

Volume of the box = (32 x 20 x 8) m3 = 5120 m3.

Question 7
A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:

A
12 kg
B
60 kg
C
72 kg
D
96 kg
Correct Answer: Option B

Volume of water displaced = (3 x 2 x 0.01) m3
= 0.06 m3.

Mass of man

= Volume of water displaced x Density of water
= (0.06 x 1000) kg
= 60 kg.

Question 8
66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:

A
84
B
90
C
168
D
336
Correct Answer: Option A

Let the length of the wire be h.

Radius = 1 mm = 1 cm. Then,
2 20

22 x 1 x 1 x h = 66.
7 20 20

h = 66 x 20 x 20 x 7 = 8400 cm = 84 m.
22

Question 9
In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:

A
75 cu. m
B
750 cu. m
C
7500 cu. m
D
75000 cu. m
Correct Answer: Option B

1 hectare = 10,000 m2

So, Area = (1.5 x 10000) m2 = 15000 m2.

Depth = 5 m = 1 m.
100 20

Volume = (Area x Depth) = 15000 x 1 m3
20

                = 750 m3.
Question 10
A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:

A
49 m2
B
50 m2
C
53.5 m2
D
55 m2
Correct Answer: Option A

Area of the wet surface:

= [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (4 x 1.25 + 6 x 1.25) + 6 x 4] m2
= 49 m2.
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