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# Area Questions

Home > Quantitative Aptitude > Area > General Questions
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The length, breadth and height of a room are in the ratio 3:2:1. If the breadth and height are halved, while the length is doubled. Then the total area of the 4 walls of the room will be decreased by

A30%

B18.75%

C15%

D13.50%

Explanation:

Given l:b:h=3:2:1

let h=10, b = 20, and l = 30 area = 2(l+b)h
area= 2*(3x+2x)*x = 2(30+20)10=1000

Now after those adjustments in the measurements, l=60, b=10, h=5
area= 2(l+b)h = 2(60+10)5=700
Percentage decrease= 1000?7001000 * 1000=30%

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A gardener changed the size of his rectangle shaped garden by increasing its length by 40% and decreasing its width by 20%. The area of the new garden

AHas increased by 12%

BHas increased by 8%

CHas increased by 20%

DCannot be expressed in % terms without actual numbers.

Explanation:

If (l*b)=x is initial area, then
New area = 1.4*l *0.8*b= 1.12*l*b= 1.12 x
Increase in area= 0.12 x
Percentage increase in area = 100*0.12x/x= 12 %

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Radius of the bigger circle is 1. Which area will be greater?

A5

B4

CCannot be determined

DNone of these

Explanation:

From the given options we can see that area marked with 4 is the answer.

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A rectangular park, 70m * 30m has two roads which are 5m wide one parallel to its length and the other to its breadth. How much will it costs to gravel the roads at rs 4 per sq.m?

ARs. 475

BRs. 1,900

CRs. 950

DRs. 1,425

Explanation:

Area of road parallel to the length= 70*5=350 sq.m.
As these two road contains common area of 5*5=25 sq.m,
so subtract once this common area, so actual area of road = 500-25 = 475
Cost to gravel @ 4 Rs./sq.m.= 475*4 = 1900 Rs.

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An isosceles triangle whose side are 13cm, 13cm, 10cm, is inscribed in a circle. Find the radius of circle

A6 cm

B7 cm

C7.04cm

D8 cm

Explanation:

a=13,b=13,c=10

s =(a+b+c)/2 = (13+13+10)/2=18

area of triangle=[18(18-13)(18-13)(18-10)]^1/2 = (18*5*5*8)^(1/2) =60 cm^2

R=(a*b*c)/(4*area of triangle)

R=(13*13*10)/(4*60)= 7.04cm

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If a circle with radius 6 cm and other circle with radius 8 cm and their centers are separated by 10 cm then what is the chord length?

A2

B6

C8.2

D9.6

EData Insuficient

Explanation:

Draw two circles asper the given data(form a triangle with sides 10,8,6)
s = (10+8+6)/2 = 12
Area = ?{12(12-10)(12-8)(12-6)} = 24
Let the height of the triangle(which is half of the chord)=h
1/2 *10*h=24
=> h=4.8
Hence length of the chord=2*4.8=9.6

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A rectangular carpet has an area of 60 sq.m. If its diagonal and longer side together equal 5 times the shorter side, the length of the carpet is:

A5m

B12m

C13m

D14.5m

Explanation:

Let, length= x meters and breadth= y meters
Then xy=60 and (x^2+y^2) + x= 5
Therefore, x=60 and (x^2 + y^2) = (5y-x)^2. Or xy=60 and 24y^2-10xy = 0.
Therefore, 24y^2 - 10 * 60 = 0 or
=> y^2 = 25
=> y = 5.
Therefore, x= (60/5)m= 12m.
So, length of the carpet = 12m

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A rectangular park, 70m * 30m has two roads which are 5m wide one parallel to its length and the other to its breadth. How much will it costs to gravel the roads at Rs. 4 per sq.m?

ARS 475

BRS 1,900

CRS 950

DRS 1,425

Explanation:

Area of road parallel to the length = 70*5 = 350 sq.m.
Area of road parallel to the breadth = 30*5 = 150 sq.m.
Total area of road = 350+150 = 500 sq.m.
As these two road contains common area of 5*5 = 25 sq.m.,
so subtract once this common area, so actual area of road = 500-25 = 475
Cost to gravel @ 4 Rs./sq.m.= 475*4 = 1900 Rs.

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12 points lie on a circle. How many cyclic quadrilaterals can be drawn by using these points?

A990

B495

C198

D110

Explanation:

Out of the 12 points lying on the circle, only 4 points can be chosen at a time to form a cyclic quadrilateral

Hence 12C4 =495 ways number of cyclic quadrilaterals are possible.

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Four concentric circles are given .The radius of 1st circle is x.next is 2x,then 3x and 4x. Given that area between 2nd and 1st is A and 4th and 3rd circles being B. Find ratio of A to B

A3:7

B7:3

C3:5

DNone of these

Explanation:

Area of first circle = pi*(x)^2 = pi*x^2
Area of second circle = pi*(2x)^2 = 4*pi*x^2
Area of third circle = pi*(3x)^2 = 9*pi*x^2
Area of fourth circle = pi*(4x)^2 = 16*pi*x^2
Area b/w 1st and 2nd circles = 3*pi*x^2
Area b/w 3rd and 4th circles = 7*pi*x^2
So, Ratio = 3:7

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