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Aptitude - Area

Exercise : Area - General Questions
1.
The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:
15360
153600
30720
307200
Answer: Option
Explanation:

Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60

Let length = 3x metres and breadth = 2x metres.

Then, 2(3x + 2x) = 1600 or x = 160.

Length = 480 m and Breadth = 320 m.

Area = (480 x 320) m2 = 153600 m2.

2.
An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
2%
2.02%
4%
4.04%
Answer: Option
Explanation:

100 cm is read as 102 cm.

A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.

(A2 - A1) = [(102)2 - (100)2]

= (102 + 100) x (102 - 100)

= 404 cm2.

Percentage error = 404 x 100 % = 4.04%
100 x 100

3.
The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
16 cm
18 cm
24 cm
Data inadequate
None of these
Answer: Option
Explanation:

2(l + b) = 5
b 1

2l + 2b = 5b

3b = 2l

b = 2 l
3

Then, Area = 216 cm2

l x b = 216

l x 2 l = 216
3

l2 = 324

l = 18 cm.

4.
The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
40%
42%
44%
46%
Answer: Option
Explanation:

Let original length = x metres and original breadth = y metres.

Original area = (xy) m2.

New length = 120 x m = 6 x m.
100 5

New breadth = 120 y m = 6 y m.
100 5

New Area = 6 x x 6 y m2 = 36 xy m2.
5 5 25

The difference between the original area = xy and new-area 36/25 xy is

= (36/25)xy - xy

= xy(36/25 - 1)

= xy(11/25) or (11/25)xy

Increase % = 11 xy x 1 x 100 % = 44%.
25 xy

Video Explanation: https://youtu.be/I3jLjLPn1W4

5.
A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
2.91 m
3 m
5.82 m
None of these
Answer: Option
Explanation:

Area of the park = (60 x 40) m2 = 2400 m2.

Area of the lawn = 2109 m2.

Area of the crossroads = (2400 - 2109) m2 = 291 m2.

Let the width of the road be x metres. Then,

60x + 40x - x2 = 291

x2 - 100x + 291 = 0

(x - 97)(x - 3) = 0

x = 3.

Video Explanation: https://youtu.be/R3CtrAKGxkc

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