Aptitude - Area - Discussion
Discussion Forum : Area - General Questions (Q.No. 4)
4.
The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
Answer: Option
Explanation:
Let original length = x metres and original breadth = y metres.
Original area = (xy) m2.
| New length = |  |
120 | x |  m |
= | |
6 | x | m. |
| 100 | 5 |
| New breadth = | |
120 | y | m |
= | |
6 | y | m. |
| 100 | 5 |
| New Area = | |
6 | x x | 6 | y | m2 |
= | |
36 | xy | m2. |
| 5 | 5 | 25 |
The difference between the original area = xy and new-area 36/25 xy is
= (36/25)xy - xy
= xy(36/25 - 1)
= xy(11/25) or (11/25)xy
 Increase % = |
|
11 | xy x | 1 | x 100 | % |
= 44%. |
| 25 | xy |
Video Explanation: https://youtu.be/I3jLjLPn1W4
Discussion:
74 comments Page 2 of 8.
Santhosh said:
1 decade ago
Let the original length be 100
so the increment on all sides by 20% i.e. length = 120
now calculate the area of original rectangle and new increased length's rectangle
i.e. A1 = 100*100= 10000 ; A2 = 120 * 120 = 14400
A2-A1 = 4400
so % increase in the area = 4400/100 = 44 %
so the increment on all sides by 20% i.e. length = 120
now calculate the area of original rectangle and new increased length's rectangle
i.e. A1 = 100*100= 10000 ; A2 = 120 * 120 = 14400
A2-A1 = 4400
so % increase in the area = 4400/100 = 44 %
Shailesh said:
9 years ago
Make it simple yar! Parentage increase increase of rectangle or square will be same.
Assume 10 x 10 original square Area will be 100 simple.
Now increase side length by 20 % will make 12 x 12 square Area will be 144.
So simple should I tell you the correct answer (C) 44.
Assume 10 x 10 original square Area will be 100 simple.
Now increase side length by 20 % will make 12 x 12 square Area will be 144.
So simple should I tell you the correct answer (C) 44.
NAVEEN said:
9 years ago
Given sides of rectangle are increased by 20%.
Let us take length L = 20.
Breadth B = 10.
Area of rectangle = LxB = 10x20 = 200.
After 20% increase L = 24.
B = 12.
Area of rectangle = LxB = 24x12 = 288.
Area increased to 288 from 200 = 44%.
Same for square.
Let us take length L = 20.
Breadth B = 10.
Area of rectangle = LxB = 10x20 = 200.
After 20% increase L = 24.
B = 12.
Area of rectangle = LxB = 24x12 = 288.
Area increased to 288 from 200 = 44%.
Same for square.
Priyanka said:
10 years ago
Let the length be 100 and breadth be 200.
So area = l*b = 20000.
If both the sides increases by 20% then,
The new length = 120 and new breadth = 240.
New area = 120*240 = 28800.
So % increase in area = (28800-20000)/20000*100 which is coming out to be 44%.
So area = l*b = 20000.
If both the sides increases by 20% then,
The new length = 120 and new breadth = 240.
New area = 120*240 = 28800.
So % increase in area = (28800-20000)/20000*100 which is coming out to be 44%.
G@ni said:
1 decade ago
I had a small and sweet solution for this problem.
The formula for % increase is x+y+xy/100.
And for %decrease is x+y-xy/100.
Now x=20.
y=20.
Therefore substituting in the above formula .
20+20+(20*20/100)=40+(400/100).
=40+4.
=44%.
The formula for % increase is x+y+xy/100.
And for %decrease is x+y-xy/100.
Now x=20.
y=20.
Therefore substituting in the above formula .
20+20+(20*20/100)=40+(400/100).
=40+4.
=44%.
Ram said:
1 decade ago
In a easy way.
Assume l & b = 10, 10.
Area = 10*10 = 100.
New length with 20% increase = 10*120/100 = 12.
So same as new breath with 20% increase = 12.
New area = 12*12 = 144.
Difference of both area = 44 %.
Assume l & b = 10, 10.
Area = 10*10 = 100.
New length with 20% increase = 10*120/100 = 12.
So same as new breath with 20% increase = 12.
New area = 12*12 = 144.
Difference of both area = 44 %.
Viki said:
8 years ago
Let us keep.
l = 100.
b = 50.
The area will be 5000
If changed be,
l = 120
b = 60
Area = 7200.
In original area, 1% of 5000 is 50.
Then changed area is 7200-5000 = 2200
Now (2200/50 = 44).
Then changed area is 44%.
l = 100.
b = 50.
The area will be 5000
If changed be,
l = 120
b = 60
Area = 7200.
In original area, 1% of 5000 is 50.
Then changed area is 7200-5000 = 2200
Now (2200/50 = 44).
Then changed area is 44%.
Gnit said:
1 decade ago
Let the area be 100.
Since length and area are proportional 20% increase in length => area = 120 since breadth and area are proportional 20 % increase in breadth => area = 144. Therefore, 144-100 = 44.
Since length and area are proportional 20% increase in length => area = 120 since breadth and area are proportional 20 % increase in breadth => area = 144. Therefore, 144-100 = 44.
AKASH SONI said:
1 decade ago
Its a lengthy approach
let length=L Breadth=b
intial area =L*B
increased length and breadth are 1.2L and 1.2B respectively
new area =1.44LB
increase area =.44lb
increased percentage area =.44LB/(LB)*100 =44%
let length=L Breadth=b
intial area =L*B
increased length and breadth are 1.2L and 1.2B respectively
new area =1.44LB
increase area =.44lb
increased percentage area =.44LB/(LB)*100 =44%
Veer said:
8 years ago
This can be solved in very simple steps. It is as follow.
The area of rectangle = l * b,
Consider initial is 100 and given that 20% increase,
100----->20%--->120----->20%---->144,
(144-100) = 44.
The area of rectangle = l * b,
Consider initial is 100 and given that 20% increase,
100----->20%--->120----->20%---->144,
(144-100) = 44.
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