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 7 of 8.
SUKUMAR SATYEN said:
1 decade ago
Let's assume Length = L cm and Breadth = B cm.
=> Area (old) = L*B = LB....equation (1).
When, Length is increased by 20%, Length = 1.2L.
When, Breadth is increased by 20%, Breadth = 1.2B.
=> Area (increased) = 1.2L*1.2B = 1.44LB.....equation (2).
Using equation (1) and (2).
=> LB (1+% increase/100) = 1.44LB.
=> % increase = (1.44-1)*100 = 0.44*100 = 44 per cent.
=> Area (old) = L*B = LB....equation (1).
When, Length is increased by 20%, Length = 1.2L.
When, Breadth is increased by 20%, Breadth = 1.2B.
=> Area (increased) = 1.2L*1.2B = 1.44LB.....equation (2).
Using equation (1) and (2).
=> LB (1+% increase/100) = 1.44LB.
=> % increase = (1.44-1)*100 = 0.44*100 = 44 per cent.
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.
Sourav said:
1 decade ago
Easiest approach:
Length 10 cm.
Breadth 10 cm.
Area = 10*10 = 100 cm.
With 20% increase:
Length 12 cm.
Breadth 12 cm.
Area 144 cm.
Percentage increase (144-100) = 44.
Ans: 44%.
Length 10 cm.
Breadth 10 cm.
Area = 10*10 = 100 cm.
With 20% increase:
Length 12 cm.
Breadth 12 cm.
Area 144 cm.
Percentage increase (144-100) = 44.
Ans: 44%.
Michelle said:
1 decade ago
Let length 40 and breadth is =20. After increasing length is 48 and breadth is 24. So the area is 1152. The difference between new are and old area is 352. So (352/800*100) = 44%.
Hema said:
1 decade ago
Why here you take length = (120/100)x and breadth = (120/100)y?
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.
Deepa ezhil. said:
1 decade ago
I can't understand Sandeepk logic. In the given problem it is given as rectangle but, he took the values of length and breadth as same value. I think the logic he used is wrong.
Rozenelle said:
1 decade ago
If the answer is 44% it is a square not a rectangle, if it is a rectangle the correct answer is 32%.
Mhbkhb said:
1 decade ago
Taking 100*100 is not correct method. Because if we take 100*100 it will bcom a square but not rectangle.
Lexinah said:
1 decade ago
What if it says each side of a square not rectangle is increased by 15%?
What is the percentage area increase in its area?
What is the percentage area increase in its area?
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