Aptitude - Area - Discussion

12. 

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

[A]. 25% increase
[B]. 50% increase
[C]. 50% decrease
[D]. 75% decrease

Answer: Option B

Explanation:

Let original length = x and original breadth = y.

Original area = xy.

New length = x .
2

New breadth = 3y.

New area = x x 3y = 3 xy.
2 2

Increase % = 1 xy x 1 x 100 % = 50%.
2 xy


Kanmani said: (Dec 11, 2010)  
Increase% = (new area-original)/original.

Sri said: (Dec 20, 2010)  
Please explain in detail.

Isn't it.

New area/original area = (3/2xy) /xy.

Arun said: (Apr 5, 2011)  
Hey sri wat kanmani told is right
see new area =3/2xy
orginal area=xy
so (3/2xy-xy)/xy=.50%(i.e)50%

Adilakshmi said: (Aug 6, 2011)  
Please explain clearly what is the formula used.

Sri said: (Aug 28, 2011)  
Thanks kanmani for your good explanation.

Xyz said: (Sep 8, 2011)  
@adilakshmi

Please see kanmani explanation

First we take

orginal length=x, new lenth=half of the orginal length
orginal breath=y, ie)l=x/2,new breath=breath is tribled
orginal area=length*breath, ie)b=3y
=xy , new area=x/2*3y=3xy/2
increase %=((new area-orginalarea)/orginal area)*100
=(3xy/2-xy)/xy [here 3/2=1.5]
=(1.5xy-xy)/xy
=(0.5xy/xy)
=0.5*100 [use 100 because to find the PERCENTAGE]
=50%

NOW ARE U CLEAR ADI?

Sundar said: (Mar 11, 2012)  
We can solve this question by simply taking an example. Let me explain.

Assume a rectangle, lxb = 4x2 and area = 8 (4*2).

New Length (after halved 4/2) = 2
New Breadth (after tripled 2*3) = 6

New area of rectangle = 2x6 = 12.

Change in area = 12 - 8 = 4.

Now % of change is 4/8*100 = 50%.

Hope this will help you. Have a nice day!

Anshu said: (Apr 4, 2012)  
ORIGINAL
LENGTH = X
BREADTH = Y
AREA = XY
----------------------------
LENGHT = 0.5X
BREADTH = 3Y
AREA = 1.5XY
THERE WAS INCREASE OF O.5 XY
0.5XY / XY * 1OO = 50%

SHORT AND CRISP METHOD

Ketan Mehta said: (Jun 9, 2012)  
@Anshu


Nice Dude!

Abc said: (Aug 27, 2012)  
How to know the area increasing or decreasing ?

Kavish said: (Jun 23, 2013)  
@Abc.

The area is obviously increasing in this case :

Take for example as given in this question.

At normal condition. When, L = x and B = y dn the area = xy,

While as per the conditions in question, L = x/2 and B = 3y dn the area = 3/2 (xy).

Dat means the area increases by 3/2 times of original area.

Further as you can see, change in area or increment in area = 3/2 (xy) -xy = 0.5xy.

Increase in percent = 0.5xy/xy *100 = 50%.

That's it.

Himanshuvijayvargia said: (Jul 12, 2013)  
x + y + x*y/100 = % increase or decrease in the area of an image when there is any increase or decrease in its sides.

Here x =(-50%); y = (200%).

-50 + 200 + (-50*200/100) = +50% answer.

Rajan Maheshwari said: (Jul 20, 2013)  
Its very simple:

Consider length and breadth to be 100.

So area should be 100 X 100 = 10,000 sq unit.

But according to given condition if length is halved then it becomes 50 (100/2) and breadth is tripled it becomes 300(100X3) So new area is 50 x 300= 1500 sq unit.

It is greater than the area if length and breadth were not altered. Therefore increase is there,

Secondly change is area is:

{(15000-10000)/10000}x 100 = 50%.

Devender said: (Jan 26, 2014)  
In the formula x+y+xy/100. Y value should be 300. How it is taken 200. I am not getting answer.

Medha said: (Jul 30, 2014)  
If we take l = 10 nd b = 10.
Area = l*b = 100.

Now the new length l/2 = 5.
And new breadth 3b = 30.

New area = 5*30 = 150.
Old area was 100 nd new is 150 so it increases by 50 which is double(new-Old = 150-100 = 50 it is 50% with respect to 100).

Means increases 50%.

Engr. Md. Easir Arafat said: (Nov 23, 2014)  
Say, length to be x and breadth to be y.

After modification: Length becomes x/2 and breadth becomes 3y.

Previous Area, A' = xy and the New Area, A = {3/2*(xy)}.

Difference in Area, A-A' = 3/2 = 1.5 hence 50% increase.

Naga said: (Feb 16, 2015)  
Assume L = 100, B = 80, L*B = 8000, Given data half length so, -50 breadth-3s = 3*80 = 240.

50*240 = 12000, change percentage = 12000-8000/80 = 50.

Sanjoy Kanrar said: (Mar 25, 2015)  
Let, length = 100 and breadth = 100.

New area:Previous area = {(100/2)*(100*3)}:{100*100}.

= 150:100.

So increase = 50%.

Aparna said: (Jun 18, 2015)  
Please explain me how the last step came.

Ash said: (Mar 30, 2016)  
Why x + y + xy/100 not taken?

Shashank said: (Oct 26, 2016)  
Assume that rectangle is 100.
Decreased by halved i.e = 50.
Increased by tripled means = 300.
So, % change is = (50 * 300)/100.
= 150.
i.e 50% more than 100.
So 50% increases.

Jo Parker said: (Mar 12, 2017)  
First of all, we all know that the area of rectangle is l*b so area(old) =lb, now according to the question it is length is halved so it is l/2 and the breadth is increased by 3times so it is 3b so by area formula it product of l and b =new area=(l/2)*(3b) =3/2(lb),so in order to find the difference we have subtract the new area from the old area so new area-old area =lb/2.

So in order to convert it to percentage multiply by 100i.e (lb)/2*(100) = 50 percent.

Migma Tshering Tamang said: (Oct 13, 2020)  
Let orginal area of rectangle is 1,
Given; L=1/2(halved) and b= 3 (tripled)
now new area= 1/2 * 3.
= 1.5.
Hence, the new area increased by 1.5-1=0.5.
So, the percentage increased by 0.5/1*100=50%.

Khadar said: (Jan 9, 2021)  
By using this method:

-50+300+((-50)(300)/100),
100%.

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