Percentage Increase and Decrease
In daily life, prices go up, temperatures drop, populations grow, and marks change from one test to the next. To describe how much something has changed, we use percentage increase and percentage decrease.
Saying "the price went up by Rs. 50" does not tell us much unless we know the original price. Rs. 50 increase on Rs. 100 is a big deal (50% increase), but Rs. 50 increase on Rs. 10,000 is tiny (0.5% increase). Percentage change gives a fair comparison by expressing the change relative to the original value.
In NCERT Class 7, percentage increase and decrease is part of the chapter Comparing Quantities. It builds on what you learned about percentages in Class 6 and connects to topics like profit & loss, discount, and simple interest.
The key idea is simple: divide the change by the original value and multiply by 100 to get the percentage change.
What is Percentage Increase and Decrease?
Definition:
- Percentage Increase: When a quantity becomes larger, the percentage by which it grows is called the percentage increase.
- Percentage Decrease: When a quantity becomes smaller, the percentage by which it reduces is called the percentage decrease.
General term — Percentage Change:
- Percentage change measures how much a value has changed compared to its original value, expressed as a percentage.
- If the new value is more than the original → percentage increase.
- If the new value is less than the original → percentage decrease.
Important:
- Percentage change is always calculated on the original value (the starting value), not the new value.
- Percentage increase and decrease are always positive numbers. The direction (increase or decrease) is stated separately.
Percentage Increase and Decrease Formula
Percentage Increase Formula:
Percentage Increase = (Increase / Original Value) × 100
Where: Increase = New Value − Original Value
Percentage Decrease Formula:
Percentage Decrease = (Decrease / Original Value) × 100
Where: Decrease = Original Value − New Value
General Formula:
Percentage Change = (Change / Original Value) × 100
Finding the new value:
- After increase: New Value = Original × (100 + Percentage) / 100
- After decrease: New Value = Original × (100 − Percentage) / 100
Finding the original value:
- After increase: Original = New Value × 100 / (100 + Percentage)
- After decrease: Original = New Value × 100 / (100 − Percentage)
Types and Properties
Types of percentage change problems:
Type 1: Finding Percentage Increase
- Given original and new (larger) values.
- Find increase, divide by original, multiply by 100.
Type 2: Finding Percentage Decrease
- Given original and new (smaller) values.
- Find decrease, divide by original, multiply by 100.
Type 3: Finding the New Value after a Given Percentage Increase
- Multiply original by (100 + percent)/100.
Type 4: Finding the New Value after a Given Percentage Decrease
- Multiply original by (100 − percent)/100.
Type 5: Finding the Original Value
- Given the new value and the percentage change, work backwards to find the original.
Type 6: Successive Percentage Changes
- When two or more percentage changes happen one after the other.
- Apply the first change, then apply the second change on the result (not on the original).
Type 7: Word Problems
- Real-life scenarios involving price changes, population growth, marks comparison, weight changes, etc.
Solved Examples
Example 1: Example 1: Simple percentage increase
Problem: The price of a notebook increased from Rs. 40 to Rs. 50. Find the percentage increase.
Solution:
Given:
- Original price = Rs. 40
- New price = Rs. 50
Step 1: Find the increase:
- Increase = 50 − 40 = Rs. 10
Step 2: Calculate percentage increase:
- Percentage increase = (10/40) × 100
- = (1/4) × 100
- = 25%
Answer: The price increased by 25%.
Example 2: Example 2: Simple percentage decrease
Problem: The temperature dropped from 35°C to 28°C. Find the percentage decrease.
Solution:
Given:
- Original temperature = 35°C
- New temperature = 28°C
Step 1: Find the decrease:
- Decrease = 35 − 28 = 7°C
Step 2: Calculate percentage decrease:
- Percentage decrease = (7/35) × 100
- = (1/5) × 100
- = 20%
Answer: The temperature decreased by 20%.
Example 3: Example 3: Finding the new value after increase
Problem: A worker earns Rs. 12,000 per month. His salary is increased by 15%. Find his new salary.
Solution:
Given:
- Original salary = Rs. 12,000
- Percentage increase = 15%
Method 1 (Two steps):
- Increase = 15% of 12,000 = (15/100) × 12,000 = Rs. 1,800
- New salary = 12,000 + 1,800 = Rs. 13,800
Method 2 (Direct formula):
- New salary = 12,000 × (100 + 15)/100 = 12,000 × 115/100 = Rs. 13,800
Answer: The new salary is Rs. 13,800.
Example 4: Example 4: Finding the new value after decrease
Problem: A shirt originally costs Rs. 800. During a sale, it is reduced by 20%. Find the sale price.
Solution:
Given:
- Original price = Rs. 800
- Percentage decrease = 20%
Using the formula:
- Decrease = 20% of 800 = (20/100) × 800 = Rs. 160
- Sale price = 800 − 160 = Rs. 640
Answer: The sale price is Rs. 640.
Example 5: Example 5: Finding the original value
Problem: After a 25% increase, the population of a town is 75,000. What was the original population?
Solution:
Given:
- New population = 75,000
- Percentage increase = 25%
Using the formula:
- Original = New Value × 100 / (100 + Percentage)
- Original = 75,000 × 100 / 125
- Original = 7,500,000 / 125
- Original = 60,000
Verification: 25% of 60,000 = 15,000. New = 60,000 + 15,000 = 75,000 ✓
Answer: The original population was 60,000.
Example 6: Example 6: Marks comparison
Problem: Rohan scored 60 marks in the first test and 75 marks in the second test. Find the percentage increase in his marks.
Solution:
Given:
- Marks in first test = 60
- Marks in second test = 75
Finding percentage increase:
- Increase = 75 − 60 = 15
- Percentage increase = (15/60) × 100
- = (1/4) × 100
- = 25%
Answer: Rohan's marks increased by 25%.
Example 7: Example 7: Successive percentage changes
Problem: The price of a toy is Rs. 500. It increases by 10% in January and then decreases by 10% in February. Find the final price. Is it the same as the original?
Solution:
Given:
- Original price = Rs. 500
Step 1: After 10% increase:
- New price = 500 × 110/100 = Rs. 550
Step 2: After 10% decrease (on Rs. 550, not Rs. 500):
- Decrease = 10% of 550 = Rs. 55
- Final price = 550 − 55 = Rs. 495
Observation: The final price (Rs. 495) is NOT equal to the original price (Rs. 500). A 10% increase followed by a 10% decrease does NOT bring us back to the original. There is a net decrease of Rs. 5 (which is 1% of the original).
Answer: Final price = Rs. 495. It is less than the original.
Example 8: Example 8: Weight loss problem
Problem: A person weighs 80 kg. After dieting, the weight reduces to 68 kg. Find the percentage decrease in weight.
Solution:
Given:
- Original weight = 80 kg
- New weight = 68 kg
Finding percentage decrease:
- Decrease = 80 − 68 = 12 kg
- Percentage decrease = (12/80) × 100
- = (3/20) × 100
- = 15%
Answer: The weight decreased by 15%.
Example 9: Example 9: Finding original from decrease
Problem: After a 30% discount, a jacket costs Rs. 1,400. Find the original price.
Solution:
Given:
- Price after 30% decrease = Rs. 1,400
- Percentage decrease = 30%
Using the formula:
- Original = New Value × 100 / (100 − Percentage)
- Original = 1,400 × 100 / 70
- Original = 1,40,000 / 70
- Original = Rs. 2,000
Verification: 30% of 2,000 = Rs. 600. After discount = 2,000 − 600 = Rs. 1,400 ✓
Answer: The original price was Rs. 2,000.
Example 10: Example 10: Comparing two changes
Problem: Shop A increases the price of a book from Rs. 200 to Rs. 250. Shop B increases the price from Rs. 300 to Rs. 360. Which shop had a higher percentage increase?
Solution:
Shop A:
- Increase = 250 − 200 = Rs. 50
- Percentage increase = (50/200) × 100 = 25%
Shop B:
- Increase = 360 − 300 = Rs. 60
- Percentage increase = (60/300) × 100 = 20%
Comparison: Even though Shop B had a larger rupee increase (Rs. 60 vs Rs. 50), Shop A had a higher percentage increase (25% vs 20%).
Answer: Shop A had the higher percentage increase (25%).
Real-World Applications
Real-world uses of percentage increase and decrease:
- Price changes: Shops display discounts as percentage decrease ("30% off"). Inflation is measured as percentage increase in prices.
- Salary and wages: Pay raises are expressed as percentage increases. "A 10% raise" means the new salary is 110% of the old salary.
- Population studies: Growth rate of a city or country is expressed as annual percentage increase.
- Academic performance: Improvement or decline in marks is measured as percentage change to compare across different totals.
- Stock market: Share prices going up or down are reported as percentage changes, making it easy to compare stocks of different values.
- Health and fitness: Weight gain or loss is often expressed as a percentage of the original body weight.
- Sports statistics: Batting averages, win percentages, and improvement rates all use percentage calculations.
Key Points to Remember
- Percentage Increase = (Increase / Original Value) × 100.
- Percentage Decrease = (Decrease / Original Value) × 100.
- Always calculate on the original (starting) value, not the new value.
- To find the new value after increase: New = Original × (100 + %) / 100.
- To find the new value after decrease: New = Original × (100 − %) / 100.
- A 10% increase followed by a 10% decrease does NOT give back the original. The result is 1% less than the original.
- In general, an x% increase followed by an x% decrease gives a net decrease of x²/100 %.
- When comparing changes, percentage change is more meaningful than absolute change.
- Successive percentage changes must be applied one after the other, not added together.
- Percentage change is always a positive number; the words "increase" or "decrease" indicate the direction.
Practice Problems
- The price of petrol increased from Rs. 80 to Rs. 92. Find the percentage increase.
- A school had 1,200 students last year. This year it has 1,050 students. Find the percentage decrease.
- A shop offers 15% discount on a bag priced at Rs. 1,600. Find the discounted price.
- After a 20% increase, the rent of a house is Rs. 18,000. What was the original rent?
- The value of a car decreases by 12% each year. If the current value is Rs. 5,00,000, find its value after one year.
- A man earns Rs. 25,000. He gets a 10% raise. After 6 months, his salary is reduced by 5%. Find his final salary.
- The population of a village increased from 8,000 to 10,000 in 5 years. Find the percentage increase.
- Priya scored 72 out of 90 in Maths and 64 out of 80 in Science. In which subject did she score a higher percentage?
Frequently Asked Questions
Q1. What is percentage increase?
Percentage increase is the amount of increase expressed as a percentage of the original value. Formula: Percentage Increase = (Increase / Original Value) × 100. For example, if a price rises from Rs. 200 to Rs. 250, the increase is Rs. 50, and the percentage increase is (50/200) × 100 = 25%.
Q2. What is percentage decrease?
Percentage decrease is the amount of decrease expressed as a percentage of the original value. Formula: Percentage Decrease = (Decrease / Original Value) × 100. For example, if weight drops from 80 kg to 72 kg, the decrease is 8 kg, and the percentage decrease is (8/80) × 100 = 10%.
Q3. Why do we divide by the original value and not the new value?
We divide by the original value because we want to know how much the value changed relative to where it started. The original value is the reference point. Dividing by the new value would give a different (incorrect) result.
Q4. Does a 20% increase followed by a 20% decrease give back the original?
No. A 20% increase followed by a 20% decrease gives a net decrease. For example, Rs. 100 → 20% increase → Rs. 120 → 20% decrease (of 120) → Rs. 96. The net result is Rs. 96, which is 4% less than the original. The general formula for the net change is −(x²/100)%.
Q5. How is percentage change different from absolute change?
Absolute change is the actual difference between new and old values (in rupees, kilograms, etc.). Percentage change expresses this difference as a percentage of the original value. Percentage change allows fair comparison when the original values are different.
Q6. Can percentage decrease ever be more than 100%?
No. Percentage decrease cannot exceed 100% because the maximum decrease is when the new value becomes 0 (100% decrease). A value cannot decrease below 0 in most real-life situations. However, percentage increase can exceed 100% (e.g., a value doubling is a 100% increase, tripling is a 200% increase).
Q7. How do you find the original value after a percentage increase?
Use the formula: Original Value = New Value × 100 / (100 + Percentage Increase). For example, if after a 25% increase the value is 500, then Original = 500 × 100 / 125 = 400.
Q8. What is the difference between percentage increase and profit percentage?
They use the same formula structure but in different contexts. Profit percentage = (Profit / Cost Price) × 100, where cost price is the 'original value' and profit is the 'increase'. Percentage increase is the general term; profit% is its application in buying and selling.
Related Topics
- Introduction to Percentage
- Profit and Loss
- Discount Calculation
- Simple Interest
- Compound Interest
- Applications of Compound Interest
- Sales Tax and VAT
- Growth and Decay
- Finding Percentage of a Number
- Converting Between %, Fraction and Decimal
- Word Problems on Comparing Quantities
- Word Problems on Profit and Loss
- Converting Percentage to Fraction
- Compound Interest (Half-Yearly & Quarterly)
