Aptitude - Area - Discussion

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%.

In the formula x+y+xy/100. Y value should be 300. How it is taken 200. I am not getting answer.

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%.

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.

@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.

How to know the area increasing or decreasing ?

@Anshu


Nice Dude!

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

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!

@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?