Aptitude

Question:
The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area?

[A].

25% increase

[B].

50% increase

[C].

50% decrease

[D].

75% decrease

Answer: Option B

Explanation:

Let original length = x and original breadth = y.

Original area = xy.

New length =	x	.
	2

New breadth = 3y.

New area =		x	x 3y		=	3	xy.
		2				2

Increase % =		1	xy x	1	x 100	%	= 50%.
		2		xy

Question:
A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is:

[A].

10%

[B].

10.08%

[C].

20%

[D].

28%

Answer: Option D

Explanation:

Let original length = x and original breadth = y.

Decrease in area	= xy – 80 x x 90 y 100 100
	= xy – 18 xy 25
	= 7 xy. 25

Decrease % =		7	xy x	1	x 100	%	= 28%.
		25		xy

Question: The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
[A].

40%

[B].

42%

[C].

44%

[D].

46%

Answer: Option C

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

Question:
The diagonal of a rectangle is 41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be:

[A].

9 cm

[B].

18 cm

[C].

20 cm

[D].

41 cm

Answer: Option B

Explanation:

l2 + b2 = 41.

Also, lb = 20.

(l + b)2 = (l2 + b2) + 2lb = 41 + 40 = 81

(l + b) = 9.

Perimeter = 2(l + b) = 18 cm.

Question:
The diagonal of the floor of a rectangular closet is 7 feet. The shorter side of the closet is 4 feet. What is the area of the closet in square feet?

[A].

5	1
	4

[B].

13	1
	2

[C].

27

[D].

37

Answer: Option C

Explanation:

Other side	=	15 2 – 9 2 2 2	ft
	=	225 – 81 4 4	ft
	=	144 4	ft
	=	6 ft.

Area of closet = (6 x 4.5) sq. ft = 27 sq. ft.

Question:
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?

[A].

16 cm

[B].

18 cm

[C].

24 cm

[D].

Data inadequate

Answer: Option B

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.

Question:
A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?

[A].

34

[B].

40

[C].

68

[D].

88

Answer: Option D

Explanation:

We have: l = 20 ft and lb = 680 sq. ft.

So, b = 34 ft.

Length of fencing = (l + 2b) = (20 + 68) ft = 88 ft.

Question:
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:

[A].

15360

[B].

153600

[C].

30720

[D].

307200

Answer: Option B

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.

Question:
The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ 26.50 per metre is Rs. 5300, what is the length of the plot in metres?

[A].

40

[B].

50

[C].

120

[D].

Data inadequate

Answer: Option E

Explanation:

Let breadth = x metres.

Then, length = (x + 20) metres.

Perimeter =		5300		m = 200 m.
		26.50

2[(x + 20) + x] = 200

2x + 20 = 100

2x = 80

x = 40.

Hence, length = x + 20 = 60 m.

Question:
The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:

[A].

1520 m2

[B].

2420 m2

[C].

2480 m2

[D].

2520 m2

Answer: Option D

Explanation:

We have: (l – b) = 23 and 2(l + b) = 206 or (l + b) = 103.

Solving the two equations, we get: l = 63 and b = 40.

Area = (l x b) = (63 x 40) m2 = 2520 m2.