Area

Area

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Question 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:
A
15360
B
153600
C
30720
D
307200
Question 1 Explanation: 
Perimeter = Distance covered in 8 min. =(12000/60)x 8m = 1600 m. 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 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:
A
2%
B
2.02%
C
4%
D
4.04%
Question 2 Explanation: 
100 cm is read as 102 cm. A1 = (100 x 100) cm2 and A2 (102 x 102) cm^2. (A2 - A1) = [(102)2 - (100)2]= (102 + 100) x (102 - 100)= 404 cm^2. Percentage error =(404/(100 x 100))x 100% = 4.04%
Question 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?
A
16 cm
B
18 cm
C
24 cm
D
Data inadequate
Question 3 Explanation: 
(2(l + b))/b=5/1 ==> 2l + 2b = 5b ==> 3b = 2l ==>b=2/3l Then, Area = 216 cm^2 l x b = 216 l x(2/3)l= 216 ==>l^2 = 324 ==> l = 18 cm.
Question 4
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
Question 4 Explanation: 
Area of the park = (60 x 40) m2 = 2400 m^2. Area of the lawn = 2109 m^2. Area of the crossroads = (2400 - 2109) m2 = 291 m^2. Let the width of the road be x metres. Then, 60x + 40x - x^2 = 291 ==> x^2 - 100x + 291 = 0 ==> (x - 97)(x - 3) = 0 ==> x = 3.
Question 5
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
Question 5 Explanation: 
Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm. Area of each tile = (41 x 41) cm^2. Required number of tiles =(1517 x 902)/(41 x 41)= 814.
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