Table of Contents

**Percentage Change Formula**

**Introduction: **

The percentage change formula is a powerful tool for understanding and analyzing changes in quantities over time. It allows us to express the difference between two values as a percentage, providing valuable insights into the magnitude and direction of the change. In this note, we will explore the percentage change formula, its applications, and how to interpret its results.

**Percentage Change Formula:**

The percentage change formula is given by:

Percentage Change = (New Value – Old Value) / Old Value) x 100.

The formula consists of three main components: the new value, the old value, and the division by the old value to find the relative change. Multiplying by 100 converts the result into a percentage.

This formula is particularly useful in various fields, including finance, economics, business, and data analysis. It enables us to assess and quantify changes in variables such as prices, quantities, sales figures, population, and more. By comparing two values and calculating the percentage change, we gain insights into the growth, trends, and fluctuations of these variables.

**Understanding Percentage Change:**

When using the formula, a positive percentage change indicates an increase or growth between the new and old values. Conversely, a negative percentage change represents a decrease or decline. The magnitude of the percentage change indicates the size or extent of the difference.

For example, let’s consider a scenario where the price of a product increased from ₹50 to ₹70. To calculate the percentage change, we apply the formula:

Percentage Change = ((₹70 – ₹50) / ₹50) x 100 = (20 / 50) x 100 = 40%.

In this case, we find a positive percentage change of 40%. This indicates a 40% increase in the price of the product.

Similarly, if the price decreased from ₹70 to ₹50, the formula would yield a negative percentage change of -28.6%, indicating a 28.6% decrease in price.

The percentage change formula allows for easy comparison and interpretation of changes across different scenarios or time periods. It enables us to determine the relative impact of the change, regardless of the actual values involved. This makes it a valuable tool for decision-making, forecasting, and understanding trends.

It’s important to note that the percentage change formula is sensitive to the choice of the base value (old value). Different reference points can yield different percentage changes. Therefore, it is crucial to select the appropriate base value to accurately represent the context or comparison being made.

**Conclusion:**

In conclusion, the percentage change formula provides a standardized approach to measure and express the difference between two values as a percentage. It is a versatile tool used in various disciplines to analyze changes in quantities, understand trends, and make informed decisions. By applying this formula, we can quantitatively assess the magnitude and direction of the change, enabling a deeper understanding of the data at hand.

**Solved Examples on Percentage Change Formula:**

**Example 1: **A company’s revenue increased from ₹500,000 to ₹600,000 in a year. Calculate the percentage change in revenue.

Solution:

Old Value = ₹500,000

New Value = ₹600,000

Percentage Change = ((₹600,000 – ₹500,000) / ₹500,000) * 100

= (₹100,000 / ₹500,000) x 100

= 20%

The revenue increased by 20%.

**Example 2:** The population of a town decreased from 10,000 to 8,000. Calculate the percentage change in population.

Solution:

Old Value = 10,000

New Value = 8,000

Percentage Change = ((8,000 – 10,000) / 10,000) x 100

= (-2,000 / 10,000) x 100

= -20%

The population decreased by 20%.

**Example 3:** The price of a stock increased from ₹50 to ₹60. Calculate the percentage change in stock price.

Solution:

Old Value = ₹50

New Value = ₹60

Percentage Change = ((₹60 – ₹50) / ₹50) × 100

= (₹10 / ₹50) × 100

= 20%

The stock price increased by 20%.

**Frequently Asked Questions on Percentage Change Formula:**

1: What is the percentage change formula?

Answer: The percentage formula is given by Percentage = (Value / Total) x 100. It is used to calculate the percentage value of a given quantity in relation to a total or reference value. This formula enables easy comparison and representation of values in terms of percentages.

2: What is the percent change when 25 is increased to 45?

Answer: To calculate the percent change when a value increases from 25 to 45, we can use the percentage change formula:

Percent Change = ((New Value – Old Value) / Old Value) x 100.

Plugging in the values:

Percent Change = ((45 – 25) / 25) x 100

= (20 / 25) x 100

= 0.8 x 100

= 80%.

Therefore, the percent change when 25 is increased to 45 is 80%.

3: How do you calculate percentage change?

Answer: To calculate the percentage change, subtract the old value from the new value to find the difference. Then divide the difference by the old value and multiply by 100 to express it as a percentage. The formula is: Percentage Change =((New Value – Old Value) / Old Value) x 100.

4: What is the difference between percent and percent increase?

Answer: Percent refers to a fraction of 100 and is used to express values relative to the whole. It is a general concept. Percent increase, however, specifically measures the relative growth between an original value and a new value. It quantifies the change in terms of a percentage. Percent increase is calculated by subtracting the original value from the new value, dividing it by the original value, and multiplying it by 100.

5: What is the difference between increase and percentage increase?

Answer: The difference between increase and percentage increase lies in the way the change is expressed. Increase refers to the actual difference or amount by which something has grown or changed. It is a numerical value. Percentage increase, on the other hand, represents the relative growth in terms of a percentage compared to the original value. It provides a standardized measure that allows for easy comparison of changes across different scales or values.

6: How to Calculate Percentage decrease?

Answer: To calculate the percentage decrease, subtract the new value from the old value to find the decrease. Then divide the decrease by the old value and multiply by 100 to express it as a percentage. The formula is: Percentage Decrease =((Old Value – New Value) / Old Value) x 100.

7: What is 25% increase from 180?

Answer: To calculate a 25% increase from a value of 180, you can use the following formula:

Increase = Value x Percentage/100

Plugging in the values:

Increase = 180 x 25/100

= 45

Therefore, a 25% increase from 180 is 45. Adding 45 to 180 gives a new value of 225.

8: How do you calculate a 10% increase?

Answer: To calculate a 10% increase from a value, you can use the following formula:

Increase = Value x Percentage/100

Let’s say you have a value of X and you want to calculate a 10% increase:

Increase = X (10/100)

This can be simplified to:

Increase = 0.1X

To find the new value after the increase, you can add the calculated increase to the original value:

New Value = X + Increase

For example, if you have a value of 100 and want to calculate a 10% increase:

Increase = 100 x 0.1 = 10

New Value = 100 + 10 = 110

Therefore, a 10% increase from 100 is 10, resulting in a new value of 110.