Aptitude - Area - Discussion
Discussion Forum : 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?
Answer: Option
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 |
Discussion:
25 comments Page 2 of 3.
Kavish said:
1 decade ago
@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.
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:
1 decade ago
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.
Here x =(-50%); y = (200%).
-50 + 200 + (-50*200/100) = +50% answer.
Rajan Maheshwari said:
1 decade ago
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%.
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:
1 decade ago
In the formula x+y+xy/100. Y value should be 300. How it is taken 200. I am not getting answer.
Medha said:
1 decade ago
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%.
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:
1 decade ago
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.
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.
(1)
Naga said:
1 decade ago
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.
50*240 = 12000, change percentage = 12000-8000/80 = 50.
Sanjoy Kanrar said:
1 decade ago
Let, length = 100 and breadth = 100.
New area:Previous area = {(100/2)*(100*3)}:{100*100}.
= 150:100.
So increase = 50%.
New area:Previous area = {(100/2)*(100*3)}:{100*100}.
= 150:100.
So increase = 50%.
(2)
Aparna said:
1 decade ago
Please explain me how the last step came.
(1)
Ash said:
9 years ago
Why x + y + xy/100 not taken?
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