Percentage Change Formula: Solved Examples

A percentage is a ratio expressed as a fraction of 100, denoted by the ‘%” symbol. Percentage change refers to expressing how much something has changed relative to its original value.

• It is calculated by dividing the change in value by the original value and then multiplying by 100.
• Percentage change formulas vary for percentage increase and percentage decrease.
• It is used to understand discounts, changes in prices, income, etc.
• The percentage change formula is used to compare different currencies and financial statements.

Percentage Change Formula = (change in value/original value) * 100

Read More: Multiplication and Division of Integers

Key Terms: Percentage, Absolute value, Percentage change formula, Discounts, Prices, Percent increase, Percent decrease

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What is Percentage Change?

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Percentage change is calculated by dividing the change by the original value and then multiplying by 100. It helps in identifying the change in the value of a thing over a period of time. 

Percentage change is used to compare changes in different quantities.

Percentage Change (%) = \(\frac{\text{New Value – Old Value}}{\text{Old Value}}\)× 100

• A positive percentage indicates an increase.
• A negative percentage indicates a decline or a decrease.

Also Read: Mass Percent Formula

Percentage Increase

Percentage increase refers to the increased change in the value of a quantity over time. 

• It is calculated by dividing the increase in value by the original value and then multiplying by 100.
• Percentage increase is a way to measure how much something has increased compared to its original value.

• When a value increases by x%, the resulting value is equal to (100 + x)% of the original amount.

It is calculated using the following formula:

Percentage Increase = [Change in value/Original value] × 100

Where Change in Value = New value – Original value

Also Read: Ratio to Percentage

Percentage decrease

Percentage decrease expresses how much something has decreased as compared to its original value.

• It is calculated by dividing the decrease in value by the original value and then multiplying by 100.
• When a value decreases by x%, the new value represents (100 – x)% of the original amount.

Percentage Decrease Formula = (decrease in value / original value) * 100

Also Read: How to Calculate Percentage

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How to Calculate Percentage Change?

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To calculate percentage change, two methods can be used.

Method 1

1. Find the difference between the two values to be compared.
2. Divide the difference by the original (old) value.
3. Multiply the result by 100 to express it as a percentage and add a “%” symbol ahead.

Example – Suppose Adam invests Rs. 100 in a stock. The price of the stock increases to Rs. 120 after one year. Calculate the percentage change in the value of his investment.

Solution: Step 1: Calculate the difference between the two values:

120-100 = 20

Step 2: Divide the difference by the original value:

20/100 = 0.2

Step 3: Multiply the result by 100 to express it as a percentage

0.2*100 = 20%

Therefore, the percentage change in the value of your investment is 20%.

Method 2

Another method to calculate the change in percentage is – 

1. The initial value is considered 100%.
2. Form a ratio where the initial value is equal to 100% and the final value is an unknown percentage (x%).
3. Initial Value/100 = Final Value/x.
4. Cross-multiply to solve for x: Initial Value × x = Final Value × 100.
5. Subtract 100% from the obtained x to find the actual percentage change.

Example – The price of a bicycle increased from INR 10,000 to INR 12,000 in a year. What is the percentage change?

Solution: Step 1: Consider the initial value as 100%.

Step 2: Form a ratio:

100%/10,000 = x%/12,000

Step 3: Cross-multiply:

100% × 12,000 = x% × 10,000

x = 120%

Step 4: Subtract 100% from the obtained x.

Percentage change = 120% - 100% = 20%

Therefore, the percentage change in the price of the bicycle is 20%.

Note:

• If a quantity is increased by r%, its final value is obtained by multiplying its initial value by (1 + r)/100.
• If a quantity is decreased by r%, its final value is obtained by multiplying its initial value by (1 – r)/100.

Solved Examples

Example 1: A person's weight increases from 60 kg to 70 kg. Calculate the percentage change.

Solution: Difference = 70 kg - 60 kg = 10 kg

Percentage change formula = (10 kg / 60 kg) * 100% = 16.67%

Therefore, their weight has increased by 16.67%.

Example 2: A smartphone is originally priced at INR 10,000, but it is currently on sale for INR 8,000. The discount is INR 2,000. The smartphone is further discounted by 10% during a special promotion. What is the percentage change in the discount?

Solution: New discount = INR 2,000 + 10% of INR 8,000

New discount = INR 2,000 + INR 800

New discount = INR 2,800

Percentage change in discount = (New discount - Old discount) / Old discount * 100%

= (2800 - 2000)/2000 * 100%

Percentage change in discount = 40%.

Example 3: Calculate the percentage decrease when 550 is reduced to 220.

Solution: Percentage decrease from 550 to 220, we can use the following formula:

Percentage decrease = (Original value - Decreased value) / Original value * 100%

Substituting the values, we get:

Percentage decrease = (550 - 220) / 550 * 100% = 330 / 550 * 100%

Percentage decrease = 60%

Also Read: Real Numbers Formula

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Things to remember

• A percentage denotes parts per hundred and is represented by the % sign.
• Percentage change is the change in a value compared to its original value, expressed as a percentage.
• Percentage change formula: (New value - Old value) / Old value * 100%
• A positive percentage change indicates an increase in value, while a negative percentage change indicates a decrease in value.
• Percentage change can be used to compare changes in different quantities over a period of time.

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