The length, breadth and height of a room are in the ratio 3:2:1. If the breadth and length are halve

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14 Dec 2016 Area

The length, breadth and height of a room are in the ratio 3:2:1. If the breadth and length are halved, while the height is doubled. Then the total area of the 4 walls of the room will:

OPtion

1) Decrease by 30%
2) Increase by 30%
3) Decrease by 18.75%
4) Increase by 18.75%
5) Decrease by 15%
6) Increase by 15%
7) Decrease by 13.6%
8) Increase by 13.6%
9) Decrease by 12.5%
10)No Change in total area of 4 walls

Solution

l:b:h=3:2:1
let h=x, b=2x and l=3x
Area of 4 walls = 2*(l+b)*h
Initial Area
Area1= 2*(3x+2x)*x = 10x^2
l2=3/2x
b2=x
h2=2x
New Area
Area2= 2*(3x/2+x)*2x = 10x^2
As Area 1 = Area 2, hence no change in area of 4 walls
Option 10)

Correct Option: 10 Best Solution (9)

Siva   8 years AGO

Area of four walls is 2(l+b)h, after changing
The area is
2[(l/2)+(b/2)]2h=2(l+b)h

Like? Yes (2) | No (1)  

Pragati Rode   8 years AGO

Let, Initially
Length (L) = 3x
Breadth (B) = 2x
Height (H) = x
Total Area of Walls = 2(BH + LH) = 2*(2x*x + 3x*x) = 2*(2x^2 +3x^2) = 10*x^2

Then, Finally
Length (L) = 3x/2 =
Breadth (B) = 2x/2 = x
Height (H) = 2x
Total Area of Walls = 2(BH + LH) = 2*(x*2x + 3x/2*2x) =
2*(2x^2+3x^2) = 10x^2

% change in Area of four walls = (Final Area - Initial Area)*100 / Initial Area

i.e. % change in Area of four walls = (10x^2- 10x^2)*100 /10x^2 =
=0
No change in total areas of 4 wall
so option is 10

Like? Yes (1) | No   

sravya   8 years AGO

The ratio: l:b:h=3:2:1
that is, length=3x, breadth=2x, height=x
let us assume x=10
so l=30,b=20,h=10
now, area of four walls=2*h(l+b)=2*10(30+20)=1000squnits

new length and breadth are halved, l=15, b=10 and new height is doubled , h=20

therefore area of four walls=2*20(15+10)=1000

So, there is no change in total area of four walls

Like? Yes (1) | No (1)  

Mathi Vanan P   8 years AGO

Area of 4 wall=2(l+b)*h
If l=3,b=2,h=1
The area is 10
After applying the condition
L=1.5,b=1,h=2
Then the area is also 10
So there is no change

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aditya trupta pattanaik   8 years AGO

area of the walls=2(lh+bh);
so by putting the values of l,b,h in the first case as 3,2,1 respectively & in the 2nd case as 1.5,1,2 respectively we get the result.

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Priya Mahanta   8 years AGO

Let's the length, breadth and height be 3x,2x,x respectively the surface area after alteration of the size will be equal to the original surface area

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ARYASREE   8 years AGO

length,breadth and height are in ratio 3:2:1 then area of 4 walls=2*h(l+b)=10
if length and breadth halved and heaight doubled then l,b,h are1.5,1,2 resp
then area=2*2*2.5=10
area remains same

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lingadurai   8 years AGO

total area of 4 wall =2*(l+b)*h
=10

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gubba ranjith kumar   8 years AGO

L:B:H::3x:2x:x
l:b:h::3/2x:2/2x:2x
2H(L+B)/2h(l+b)
=1

Like? Yes | No (1)