Percentage Change is the ratio of change in the value to the original value multiplied by 100. Percentage is defined as a number or ratio expressed as a fraction of 100. The word percentage is derived from the Latin word per centum which means “by the hundred”.
The percentage is depicted using the symbol “%“. Percentage change is found when there is a change in any number. Percentage Increase and Percentage Decrease both are calculated in Percentage Change.
In this article, we will learn about, Percentage Change, Percentage Formula, Percentage Change Formula, Examples of Percentage increase & Decrease, etc in detail.
What is Percent Change?
Percentage change is the difference between a number and the new number taken as the ratio to the original number multiplied by 100. For, example suppose 5 is increased to 10 then the percent change is calculated as, (10 – 5)/5 × 100% = 100%
Percentage Change Definition
Percentage change is defined as the ratio of the change in the value by the original value multiplied by a hundred. The percentage change gives the difference in quantity out of 100.
Percentage is calculated by dividing the given value by the total value and multiplying the result obtained by 100.
Percentage (%) = (Given Value / Total Value) × 100 %
Percentage change is calculated when there is a change in the value of a quantity over a period of time. Percentage change is calculated in terms of percentage increase and percentage decrease. For calculating the percentage change, we have to divide the change in value by the original value and then multiply the obtained value by 100.
Percentage Change = [Change in Value / Original Value] × 100
where,
Change in Value = (New Value – Original Value)
Percentage Increase
Percentage increase means the percentage change in the value of a quantity when it is increased over a period of time. It is calculated by subtracting the original value from the new value, dividing it by the original value, and then multiplying the resultant with 100. The formula for the percentage increase is given as,
Percentage Increase = [(New value – Original value)/Original value] × 100
Note: If a value is increased by x% then the new value is (100 + x)% of the original amount.
Percentage Decrease
Percentage decrease means the percentage change in the value of a quantity when it is decreased over a period of time. It is calculated by subtracting the new value from the original value, dividing it by the original value, and then multiplying the resultant by 100. The formula for the percentage decrease is given as,
Percentage Decrease = [(Original value – New value)/Original value] × 100
Note: If a value is decreased by x%, then the new value is (100 – x)% of the original amount.
How to Find Percent Change?
To calculate a percentage change, use the method discussed below:
Step 1: Find the change between the two values.
Step 2: Divide the answer obtained in Step 1 by the original value.
Step 3: Change the value obtained in step 2 to the percentage by multiplying by 100 and adding the sign “%”
Example: A number is increased from 10 to 15 then find the percentage change.
Original Value = 10
Increased Value = 15
Change in Value = 15 – 10 = 5
- Percentage Change = (change in value) / (original value) × 100
Percentage Change = (5 / 10) × 100 = 50 %
How to Change to Percent?
Any given value can be easily converted to the percentage value by simply multiplying the given value with 100 and adding a percentage(%) sign. The percentage value can easily be calculated using the percentage calculator added above.
Example: Convert 15.8 into percentage.
15.8 × 100
= 1580%
Percentage Change to Fraction
To change a percent to a fraction, put the percentage over 100 (after removing the % sign) and simplify it. For example, to convert 21% to a fraction, put 21 over 100, like this: 21/10
Percentage Change Examples
Example 1: A boy obtained 820 marks in an examination out of 900 marks. Calculate the percentage of the marks obtained by the boy.
Solution:
Given,
- Number of marks obtained = 820
- Maximum marks = 900
Percentage of marks = (820/900) × 100
Percentage = (0.9112) × 100
Hence, the percentage of marks obtained by the boy is 91.12%
Example 2: Geeta’s weight is 25% more than that of Fathima. If Fathima’s weight is 56 kg, then how much percent of Fathima’s weight is less than that of Geetha?
Solution:
Given,
- Fathima’s weight = 60 kg
- Geetha’s weight is 25% more than that of Fathima.
Hence, Geetha’s weight = 56 + 56 × (¼) = (56 + 16) kg = 72 kg.
Required percentage = [(72 – 56)/72] × 100 =22.22%
Hence, the weight of Fathima is 22.22% less than that of Geetha.
Example 3: Calculate the percentage increase if the price of the cooking oil of ₨ 150 increased to ₨ 180.
Solution:
Given,
- Original price of the oil = ₨ 150
- New price of the oil = ₨ 180
Change in the value of price = ₨ 180 – ₨ 150 = ₨ 30
Percentage increase = [(change in value)/original value] × 100
Percentage increase = (30/150) × 100 = 20 %
Hence, the percentage increase in the price of the cooking oil is 20%
Example 4: The price of a mobile phone increases every year by 20%. If the present price is ₨ 15000, then what was the price (in ₨.) 3 years ago?
Solution:
Let the price of the mobile phone 3 years ago be P
Price of the mobile phone, 2 years ago = P + 20% of P = P + (20/100)P = 1.20P
Price of the mobile phone, one year ago = 1.20 P + 20% of (1.2 P) = 1.20 P + 0.24P = 1.44 P
Present price of the mobile = 1.44 P + 20% of (1.44 P) = 1.44 P + 0.288 P = 1.728 P
1. 728 P = 15000
P = ₨ 8680.55
Hence, the price of the mobile phone 3 years ago was ₨ 8680.55
Example 5: Ravi’s savings amount was ₨ 5000 in the month of January. His savings decreased to ₨ 3800 in the month of February. Calculate the percentage decrease in his savings.
Solution:
Given,
- Ravi’s savings amount in January = 5000
- Ravi’s savings amount in February = 3800
Decrease in his savings = 5000 – 3800 = 1200
Percentage decrease = [(decreased savings)/original value] × 100
Now, percentage decrease in his savings = (1200/5000) 100 = 24%
Example 6: A number is increased by 25% and then decreased by 25%. Find the net increase or decrease percent.
Solution:
Let the number be 100
Number is increased by 25%
We know that, if a value is increased by x% then the new value is (100 + x)% of the original amount.
Now, the increased number = (100 + 25)% of 100 = (125/100) × 100 = 125
Number is now decreased by 25%
We know that, if a value is decreased by x%, then the new value is (100 – x)% of the original amount.
Now, the decreased number = (100 – 25)% of 125 = (75/100) ×125 = 93.75
Net decrease = 100 – 93.75 = 6.25
Hence, the number is decreased by 6.25%
Example 7: What is a 20% increase from 80?
Solution:
If a number is increased by 20% it is 120% of itself
Now,
- 120% of 80 = 120 / 100 × 80 = 96
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Practice Problems on Percentage Change
1. The price of a laptop was $800 last year. This year, the price has increased to $960. Calculate the percentage increase in the price of the laptop.
2. A stock was valued at $350 per share at the beginning of the week. At the end of the week, its value dropped to $280 per share. What is the percentage decrease in the stock’s value?
3. A small town had a population of 20,000 people. Over the decade, the population grew to 25,000. What is the percentage increase in the population?
4. A store sells a jacket for $120. During a sale, the price is reduced to $90. What is the percentage decrease in the price of the jacket?
FAQs on Percentage Change
How to Calculate Percent Change?
The formula for calculating percentage change is,
Percentage Change = (change / initial) × 100
What does Percentage Change tells you?
Percentage change tells us about the change which occurs when the initial value is increased or decreased with respect to the initial value in terms of percentage.
What is an Example of Percentage Change?
The concept of percentage change can easily be understood by the following example, suppose the salary of Kabir changes from 100000 to 150000 then we say that Kabir’s salary is increased by 50%.
What is Percentage change when 25 is increased to 45?
Percentage change when 25 is increased to 45 is calculated as
- Initial Value = 25
- Final value = 45
Change in Value = 45 – 25 = 20
Percentage Change = (change / initial) × 100 = 20/25 × 100 = 80%
What Percentage Increase?
When the value of any number increases we calculate the percentage increase of that value with respect to the original value using the formula,
Percentage Increase = [New Value – Original Value]/[Original Value] × 100
How to Calculate Percentage Increases?
Percentage Increase is calculated using the formula, Percentage Increase = [New Value – Original Value]/[Original Value] × 100
How do you Calculate Rate of Change?
Rate of change is calculated using the formula, (y2 – y1)/(x2 – x1) where (x1, y1) and (x2, y2) are initial and final point respectively.
What is Percentage Calculator?
Percentage change calculator is a tool that is used to calculate the percentage change between two numbers.
How to Calculate Percentage Increase salary?
Percentage Increase salary is calculated bu using the formula, Salary Increase = (Increased Salary – Initial Salary)/Initial Salary × 100%
What is Relative Percent Change?
Relative Percentage Change is calculated using the formula, Relative Change = (New Value – Old Value) / Old Value × 100%
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