# Aptitude - Area - Discussion

### Discussion :: Area - General Questions (Q.No.12)

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

Explanation:

Let original length = x and original breadth = y.

Original area = xy.

 New length = x . 2

 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%.