The length, breadth and height of a room are in the ratio 9:7:5. If the breadth and length are doubl

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11 Jan 2018 Area

The length, breadth and height of a room are in the ratio 9:7:5. If the breadth and length are doubled while the height is halved. Then the total area of the 4 walls of the room will:

OPtion

1) Increase by 10%
2) Increase by 22%
3) Increase by 25%
4) Increase by 15%
5) Increase by 7%
6) Increase by 20%
7) Increase by 9%
8) Increase by 0%
9) Increase by 8%
10)None of these

Solution

l:b:h=9:7:5


Area of 4 walls = 2*(l+b)*h

Inital Area:
Let h=5x, b=7x and l=9x
Area of 4 walls = 2*(9x+7x)*5x = 160x^2

New dimensions when the breadth and length are doubled while the height is halved
l1=18x
b1=14x
h1=2.5x

New Area
Area2= 2*(18x+14x)* 5x/2x = 160x^2
% Increase in area = (160-160)*100/160 = 0%

Option 8)

Correct Option: 8 Best Solution (8)

Dr.Dipin Singh   6 years AGO

Initial area of four walls = (9x*2+7x*2)*5x= 160 x^2
New area after changes = (18x*2+14x*2)*5x/2= 160 X^2
Hence area will increase by 0% as there is no change in area of four walls.

Like? Yes (3) | No   

Suman   6 years AGO

Earlier Area of 4 walls = 2*(l*h+b*h)
Now Area of 4 walls= 2*(2l*h/2+2b*h/2)= 2*(l*h+b*h)
so no change in area of walls.
0% change

Like? Yes (2) | No   

Varun   6 years AGO

A room will have 4 walls
Each wall associated with height, let h
And each of the 2 walls associated with length and breadth, let l and b respectively.
So area of 4 walls = hl+hl+hb+hb
=2hl + 2hb......(1)

Later, length and breadth are doubled and height halved
= 2(h/2)(2l) + 2(h/2)(2l)
= 2hl + 2hl........(2)

From (1) and (2) area are same,
That means 0% increased,
= Option 8)

Like? Yes | No (1)  

SAYAN CHATTERJEE   6 years AGO

Initially the area of the walls were 5*9*2+5*7*2= 160 units
Now, the area is 5/2*18*2+ 5/2*14*2 = 160 units.
Option 8.

Like? Yes | No (1)  

Jayant bhadani   6 years AGO

area of 4 wall room =2*h*(l+b)
therefore area =2*5*(9+7) =160
if length and breadth is double and height is halved then area =2*2.5*(18+14)=160

Like? Yes | No (1)  

Shreya   6 years AGO

Since area of 4 walls = 2(l+b)*h
the difference between original and new area is zero.

Like? Yes | No (1)  

shanmukha   6 years AGO

we have l=9 b=7 h=5
area of 4 walls=2h(l+b)=2*5(9+7)=160
now,l=18 b=14 h=2.5
area of 4 walls=2h(l+b)=2*2.5(18+14)=160
hence, option->8 increases by 0%

Like? Yes | No (1)  

AYAN PAUL   6 years AGO

Let the Length Breadth and Height respectively are 9 , 7 & 5 Unit
So area of the 4 wall will be = 2(9+7)*5 = 160
In Second case area will be = 2(18+14)*2.5 = 160
So area increases by 0%

Like? Yes | No (2)