Percentage Increase and Decrease
Percentage increase and percentage decrease describe how much a quantity has grown or shrunk relative to its original value. These concepts are used in everyday life for price changes, population growth, test scores, and discounts.
If the price of a toy goes up from ₹200 to ₹250, the increase is ₹50 and the percentage increase is (50/200) × 100 = 25%. If it goes down from ₹200 to ₹160, the decrease is ₹40 and the percentage decrease is (40/200) × 100 = 20%.
What is Percentage Increase and Decrease - Class 5 Maths (Percentage)?
Percentage Increase: The amount by which a value has grown, expressed as a percentage of the original value.
Percentage Decrease: The amount by which a value has reduced, expressed as a percentage of the original value.
Percentage Increase and Decrease Formula
Percentage Increase = (Increase / Original Value) × 100
Percentage Decrease = (Decrease / Original Value) × 100
New Value after x% increase = Original + (x/100 × Original)
New Value after x% decrease = Original − (x/100 × Original)
Solved Examples
Example 1: 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: 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: 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: 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: 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: 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.
Example 7: Example 7: Weight loss
Problem: Kavi's weight decreased from 50 kg to 45 kg. Find the percentage decrease.
Solution:
Decrease = 50 − 45 = 5 kg
Percentage decrease = (5/50) × 100 = 10%
Answer: Kavi's weight decreased by 10%.
Example 8: Example 8: Marks comparison
Problem: Priya scored 60 marks in the first test and 75 marks in the second. What is the percentage increase?
Solution:
Increase = 75 − 60 = 15
Percentage increase = (15/60) × 100 = 25%
Answer: Priya's marks increased by 25%.
Example 9: Example 9: Word problem — Savings
Problem: Rahul saved ₹800 last month. This month he saved 10% less. How much did he save this month?
Solution:
Decrease = 10% of 800 = 80
This month = 800 − 80 = 720
Answer: Rahul saved ₹720 this month.
Key Points to Remember
- Percentage increase = (Increase ÷ Original) × 100.
- Percentage decrease = (Decrease ÷ Original) × 100.
- Always use the original value as the base for calculating percentage change, not the new value.
- To find the new value after increase: add the percentage amount to the original.
- To find the new value after decrease: subtract the percentage amount from the original.
- A 50% decrease halves the value; a 100% increase doubles the value.
- Percentage change can be used for prices, populations, weights, marks, and any measurable quantity.
Practice Problems
- The price of rice went from ₹40/kg to ₹50/kg. Find the percentage increase.
- A shop had 200 customers on Monday and 170 on Tuesday. Find the percentage decrease.
- A toy costs ₹350. It is marked up by 20%. What is the new price?
- An item priced at ₹800 is sold at a 15% discount. Find the selling price.
- A school's enrolment rose from 1,200 to 1,500. Find the percentage increase.
- After a 30% decrease, the population of a colony is 7,000. What was the original population?
- Dev scored 45 marks in the first test and 54 in the second. Find the percentage increase in his marks.
- A train ticket costs ₹250. The fare increases by 12%. What is the new fare?
Frequently Asked Questions
Q1. What is percentage increase?
Percentage increase measures how much a value has grown compared to its original value, expressed as a percentage. Formula: (Increase ÷ Original) × 100. For example, going from 50 to 65 is a 30% increase.
Q2. What is percentage decrease?
Percentage decrease measures how much a value has reduced compared to its original value, expressed as a percentage. Formula: (Decrease ÷ Original) × 100. For example, going from 80 to 60 is a 25% decrease.
Q3. Why must I use the original value as the base?
The original value is the reference point. Percentage change compares the change to where you started. Using the new value would give a different (incorrect) percentage.
Q4. Can the percentage decrease be more than 100%?
No. A 100% decrease means the value becomes 0. You cannot decrease by more than 100% because the result would be negative, which does not apply to quantities like price or population.
Q5. Can the percentage increase be more than 100%?
Yes. A 100% increase means the value doubles. A 200% increase means it triples. For example, if ₹100 increases by 150%, the new amount is ₹250.
Q6. How is percentage decrease related to discounts?
A discount is a percentage decrease in price. A 20% discount on ₹500 means the price decreases by 20% of 500 = ₹100, so the new price is ₹400.
Q7. If a price increases by 20% and then decreases by 20%, is it back to the original?
No. The base changes after the first change. ₹100 + 20% = ₹120. Then ₹120 − 20% = ₹120 − ₹24 = ₹96. The final price (₹96) is less than the original (₹100).
Q8. Is this topic in the NCERT Class 5 syllabus?
Yes. Percentage increase and decrease are part of the Percentage chapter in the NCERT Class 5 Maths curriculum and are commonly tested in school examinations.
