Area

Question:
A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 75 paise per sq. m, is:

[A].

Rs. 456

[B].

Rs. 458

[C].

Rs. 558

[D].

Rs. 568

Answer: Option C

Explanation:

Area to be plastered	= [2(l + b) x h] + (l x b)
	= {[2(25 + 12) x 6] + (25 x 12)} m2
	= (444 + 300) m2
	= 744 m2.

Cost of plastering = Rs.		744 x	75		= Rs. 558.
			100

Question:
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:

[A].

2%

[B].

2.02%

[C].

4%

[D].

4.04%

Answer: Option D

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

Question:
A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?

[A].

20

[B].

24

[C].

30

[D].

33

Answer: Option C

Explanation:

Let the side of the square(ABCD) be x metres.

Then, AB + BC = 2x metres.

AC = 2x = (1.41x) m.

Saving on 2x metres = (0.59x) m.

Saving % =		0.59x	x 100	%	= 30% (approx.)
		2x

Question:
What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?

[A].

814

[B].

820

[C].

840

[D].

844

Answer: Option A

Explanation:

Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.

Area of each tile = (41 x 41) cm2.

Required number of tiles =		1517 x 902		= 814.
		41 x 41

Question: 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?
[A].

2.91 m

[B].

3 m

[C].

5.82 m

[D].

None of these

Answer: Option B

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

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.