# Percent change

If the length of a rectangle is increased by 25% and the width is decreased by 10%, the area of the rectangle is larger than the area of the original rectangle by what percent?

Result

p =  12.5 %

#### Solution:

$q_{1}=1+25/100=\dfrac{ 5 }{ 4 }=1.25 \ \\ q_{2}=1-10/100=\dfrac{ 9 }{ 10 }=0.9 \ \\ \ \\ S_{1}=ab \ \\ S_{2}=(a \cdot \ q_{1}) \cdot \ (b \cdot \ q_{2}) \ \\ \ \\ p=100 \cdot \ \dfrac{ S_{2}-S_{1} }{ S_{1} } \ \\ \ \\ p=100 \cdot \ \dfrac{ (a \cdot \ q_{1}) \cdot \ (b \cdot \ q_{2}) - ab }{ ab } \ \\ \ \\ p=100 \cdot \ \dfrac{ q_{1} \cdot \ q_{2}-1 }{ 1 }=100 \cdot \ \dfrac{ 1.25 \cdot \ 0.9-1 }{ 1 }=\dfrac{ 25 }{ 2 }=12.5=12.5 \%$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Tips to related online calculators

## Next similar math problems:

1. Diameters of circles
How many percent of the area of a larger circle is a smaller circle if the smaller circle has a diameter 120 mm and a larger one has a diameter 300 mm?
2. Researchers
Researchers ask 200 families whether or not they were the homeowner and how many cars they had. Their response was homeowner: 14 no car or one car, two or more cars 86, not homeowner: 38 no car or one car, two or more cars 62. What percent of the families
3. Parcel
Both dimensions of the rectangular parcel were increased by 26%. By how many % has increased its acreage?
4. Price increase 2x
If two consecutive times we increase the price of the product by 20%, how many % is higher final price than the original?
5. Percentage increase
Increase number 400 by 3.5%
6. Profit gain
If 5% more is gained by selling an article for Rs. 350 than by selling it for Rs. 340, the cost of the article is:
7. Summerjob
The temporary workers planted new trees. Of the total number of 500 seedlings, they managed to plant 426. How many percents did they meet the daily planting limit?
8. Mixed with percentages
Calculate 33 1/3% of 570.
9. Lathe
95% of the components manufactured on the lathe comply with the standard, of which 80% of the components are first-class. How likely can we expect a manufactured part to be first class?
10. Fruit tea
Tea contains 7% of fruit components and 12% of sugar in this component. How many percents of sugar is represented in the whole tea?
11. Borrowing
I borrow 25,000 to 6.9% p.a.. I pay 500 per month. How much will I pay and for how long?