M4maths Previous Puzzles

02 Feb 2017 Area

The length, breadth and height of a room are in the ratio 7:3:1. If the breadth and height are doubled while the length is halved. Then the total area of the 4 walls of the room will:

OPtion

1) Increase by 30%
2) Increase by 40%
3) Increase by 50%
4) Increase by 60%
5) Increase by 70%
6) Increase by 80%
7) Increase by 90%
8) Increase by 18%
9) Increase by 10%
10)No Change in total area of 4 walls

Solution

l:b:h=7:3:1
let h=x, b=3x and l=7x
Area of 4 walls = 2*(l+b)*h
Initial Area
Area1= 2*(7x+3x)*x = 20x^2
New dimensions
l2=7x/2
b2=6x
h2=2x
New Area
Area2= 2*(7x/2+6x)* 2x = 38x^2
% Increase in area = (38-20)*100/20 = 90%
Option 7)

Correct Option: 7 Best Solution (16)

G.S.Kantharao   8 years AGO

Let l,b,h=7x,3x,x
4 walled area = 2h(l+b)
=2x(7x+3x) = 20x^2
When dimensions changed 3.5x,6x,2x
New Area= 2*2x(3.5x+6x)= 38x^2
Difference= 18x^2
% of increase= (18x^2*100)/20x^2 = 90%
Hence right option is 7.

Like? Yes (8) | No   

madanpal vishwakarma    8 years AGO

let assume that
height of the room is h = x
length l =7x
breadth b =3x

So the area of room = 2 h (l+b) = 2x(7x+3x) =20 x^2

As per question increasing height into double = 2 x
breadth = 6x
length =7x/2

so the new area of room = 2 h(l+b) = 2 *2x ((7x/2)+6x)=38x^2

clearly the area 38x^2 increased by 90 % of previous area 20x^2

Like? Yes (5) | No (1)  

DHANANJAY KUMAR   8 years AGO

length, breadth, height ratio is 7:3:1
then surface area of 4 side wall is 2*(7*1+3*1)=20
if length is halved, breadth and height is doubled then ratio is 7/2:6:2
then surface area is 2((7/2*2)+6*2)=38
difference is 18 and increase percentage is 18/20*100=90%

Like? Yes (2) | No   

DIVYANSHU SHEKHAR   8 years AGO

Original l=7m,b=3m,h=1m
area of 4walls=2h(l+b)=2*1[7+3]=20sq.mt
New l=3.5m,b=6m,h=2m area of 4walls=2*2[3.5+6]=38sq.mt
%change=(38-20)*100/20= 90% increase

Like? Yes (1) | No   

TUSHANT LATARE   8 years AGO

let length,breadth & height of room be 7, 3 &1unit respt.
Area of walls= 2 ( l+b) *h= 2( 7+3 )*1=20 sq.unit
Now length,breadth,height of room become 7/2, 6 & 2 unit resp.
Area of walls = 2( 7/2+6)*2=38 sq. unit.
% increase in area of walls =(38-20)*100/20=90%.

Like? Yes (1) | No   

somveer   8 years AGO

Let, initially
Length =7
breadth =3
Height=1
total area of wall = 2h(b+l)=2×1(7+3)=20
then, finally
Length =3.5
Breadth =6
Height =2
again total area of walls=2×2(3.5+6)=38
%Change of wall area=(finally area-initially area)*100/initially area
=(38-20)100/20
=90%

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gubba ranjith kumar   8 years AGO

2.2h(7/2h+6h)/2h(7h+3h)
=38/20 implies 90% increase

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Basant Bothra   8 years AGO

First,
L=7,B=3,H=1
Area=20 sqUnit
Then=
L=3.5,B=6,H=2
Area=38
Area=(38-20)/20=90% In

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Bruce wayne   8 years AGO

l. b. h
7. 3. 1

Area of wall: 2(lh+bh) =20

Now
l. b. h
3.5. 6. 2

Area: 2(lh+BH)=38

Change in area: (38-20)*100/20 = 90percent

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Anandita Rani   8 years AGO

area of 4 wall = 20 x^2
area of 4 wall after change = 38 x^2
change percentage = 38x^2 - 20x ^2 / 20x^2 *100 = 90%

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SATHEESH V   8 years AGO

Let us take l=7x , b=3x , c=x
area of 4 walls= (l+b)*h = 10(x^2)

now l=7x/2 , b=6x , h=2x
area of 4 walls=19x^2

percentage change= {[ (19-10)x^2 ]/10x^2}*100
% change= +90%

therefore increases by 90%

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RANJEET KUMAR   8 years AGO

Initial area = 20
Changed area=38
% change = (18/20)*100= 90%

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Ajay Sharma   8 years AGO

let length be 70.breadth=30 and height =10
then area of two walls =2*70*10=1400
area of other two walls= 2*30*10=600
total area=2000
if length is halfed and breadth and height are doubled
then length is 35,height 20 and breadth 60
area of two walls=2*35*20=1400
area of other two walls=2*60*20=2400
total area = 3800
so increase in area is 90%

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Mukund Manohar   8 years AGO

Let the length, breadth & height be 7,3 and 1 unit respectively
Area of walls = 2 (7+3)*1 = 20 Sq. Units
Now,length=3.5,breadth=6 & height = 2
Area= 2 (3.5+6)*2 = 38 sq.units
%increase=(38-20)*100/20 = 90
Total area of the 4 walls of the room will increase by 90%

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amit kumar   8 years AGO

let length =7x
breadth=3x
height=x
A(area of 4 walls)=2*(l+b)*h
2*(7x+3x)*x
20x^2
now new length=7x/2
breadth=6x
height=2x
new area=2*[(7x/2)+6x]*2x
=38x^2
increased % in area=(18x^2/20x^2)*100
=90%

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RAHUL KUMAR SINGH   8 years AGO

formula for calculating area of 4 walls=2(l+b)h
orignal area=20
new area after change in dimensions=38
so,incr. in area=((38-20)/20)*100=90

Like? Yes | No (1)