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Area
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:

Answer:Option 1

Explanation:

Solution:
Perimeter = Distance covered in 8 min. =
(1200060×8)m=1600m
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Therefore Length = 480 m and Breadth = 320 m.
Therefore Area = (480 x 320) m2 = 153600 m2.

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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:

Answer:Option 1

Explanation:

Solution:
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 =
(404100×100×100)%=4.04%

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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?

Answer:Option 1

Explanation:

Solution:
2(l+b)b=512l+2b=5b3b=2lb=23lThen,Area = 216cm2l×b=216l×23l=216l2=324l=18cm

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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?

Answer:Option 1

Explanation:

Solution:
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.

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5.The diagonal of the floor of a rectangular closet is 7 1/2 feet. The shorter side of the closet is 4 1/2 feet. What is the area of the closet in square feet?

Answer:Option 1

Explanation:

Solution:
OuterSide=(152)2(92)2ft=2254814ft=1444ft=6ftAreaofcloset=(6×4.5)sq.ft=27sq.ft.

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6.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:

Answer:Option 1

Explanation:

Solution:
Letoriginallength=xandoriginalbreadth=yDecreaseinarea=xy(80100x×90100y)=(xy1825xy)=725xyDecrease%=(725xy×1xy×100)%=28%

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

Answer:Option 1

Explanation:

Solution:
Let the side of the square(ABCD) be x metres.
Area mcq solution image
AC = √2x = (1.41x) m.
Saving on 2x metres = (0.59x) m.
Area mcq solution image

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8.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?

Answer:Option 1

Explanation:

Solution:
Lengthoflargesttile=H.C.F.of1517cmand902cm=41cmAreaofeachtile=(41×41)cm2Requirednumberoftiles=(1517×90241×41)=814

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

Answer:Option 1

Explanation:

Solution:
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.

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

Answer:Option 1

Explanation:

Solution:
Letoriginallength=xandOriginalbreadth=yOriginalarea=xyNewlength=x2Newbreadth=3yNewarea=(x2×3y)=32xyIncrease%=(12xy×1xy×100)=50%

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