Class 8 - Percentage Increase Or Decrease

Percentage increase and decrease are everywhere in real life. When your parents talk about salary hikes, when shops announce sales, when news reports inflation rates, or when your phone battery drops percentages are working behind the scenes. We can compare different quantities when there is an increase or a decrease in their values. The amounts can be compared better if expressed as a percentage. Consider the following statements.

There is a 10% increase in the number of applicants for the exam.

The price of petrol increased by 1%.

The number of votes decreased by 6%.

Statements like the ones given above gives a better understanding of how much a quantity increased or decreased.

Steps to calculate increase or decrease in percent

• Step 1: Find the increase or decrease of quantity.
• Step 2: Write this as a fraction with a denominator as the original quantity.
• Step 3: Multiply with 100 and put the % symbol.

$\text{Percentage Change} = \frac{\text{Change}}{\text{Original}} \times 100$

Also use: Percentage Calculator

Table of Contents

• Percentage Increase
• Percentage Decrease
• Percentage Increase Decrease Solved Examples
• Frequently Asked Questions on Percentage increase decrease

Percentage Increase

Percentage increase tells you how much something has grown compared to its original value. It measures the growth as a percentage. When a value becomes bigger, the increase shown as a percentage of the original value is called percentage increase.

• Formula for Percentage Increase:$\text{Percentage Increase} = \frac{\text{Increased Value} - \text{Original Value}}{\text{Original Value}} \times 100$

Percentage Decrease

Percentage decrease tells you how much something has become smaller compared to its original value. It measures the reduction as a percentage. When a value becomes smaller, the decrease shown as a percentage of the original value is called percentage decrease.

• Formula for Percentage Decrease:$\text{Percentage Decrease} = \frac{\text{Original Value} - \text{Decreased Value}}{\text{Original Value}} \times 100$

Percentage Increase Decrease Solved Examples

Example 1: Finding percentage increase

Problem: A book's price increased from ₹150 to ₹180. Find the percentage increase.

Solution:

Step 1: Increase = 180 − 150 = ₹30

Step 2: Percentage increase = (30/150) × 100 = 20%

Answer: The price increased by 20%.

Example 2: Finding percentage decrease

Problem: The number of students absent decreased from 40 to 30. Find the percentage decrease.

Solution:

Step 1: Decrease = 40 − 30 = 10

Step 2: Percentage decrease = (10/40) × 100 = 25%

Answer: The absentees decreased by 25%.

Example 3: Finding new value after increase

Problem: A shirt costs ₹400. If the price increases by 15%, what is the new price?

Solution:

Step 1: Increase = 15% of 400 = (15/100) × 400 = ₹60

Step 2: New price = 400 + 60 = ₹460

Answer: The new price is ₹460.

Example 4: Finding new value after decrease

Problem: A school bag is priced at ₹600. During a sale, the price decreases by 20%. What is the sale price?

Solution:

Step 1: Decrease = 20% of 600 = (20/100) × 600 = ₹120

Step 2: Sale price = 600 − 120 = ₹480

Answer: The sale price is ₹480.

Example 5: Population growth

Problem: A village had 5,000 people. The population grew by 12%. What is the new population?

Solution:

Increase = 12% of 5,000 = 600

New population = 5,000 + 600 = 5,600

Answer: The new population is 5,600.

Example 6: Finding original value

Problem: After a 25% increase, a jacket costs ₹500. What was the original price?

Solution:

Step 1: After 25% increase: Original + 25% of Original = 500

Step 2: 125% of Original = 500

Step 3: Original = 500 × 100/125 = ₹400

Answer: The original price was ₹400.