📊 Percentages
Learn the concept, formulas,
shortcuts and problem-solving
techniques for percentages.
📖 1. Concept
Percentage means
"per hundred".
The symbol used for percentage is
%.
20% = 20 / 100 = 1 / 5
Therefore:
20% of 500
= (20 / 100) × 500
= 100
📌 2. Important Formulas
Percentage =
(Part / Whole) × 100
Part =
(Percentage / 100) × Whole
Percentage Increase =
(Increase / Original Value) × 100
Percentage Decrease =
(Decrease / Original Value) × 100
🧮 3. Solved Examples
Example 1
Find 20% of 500.
20% of 500
= (20 / 100) × 500
= 100
✅ Answer: 100
Example 2
A student scored 72 marks
out of 90.
Find the percentage.
Percentage
= (72 / 90) × 100
= 80%
✅ Answer: 80%
Example 3
A number increases from
200 to 240.
Find the percentage increase.
Increase
= 240 - 200
= 40
Percentage Increase
= (40 / 200) × 100
= 20%
✅ Answer: 20%
⚡ 4. Shortcuts
10%
→ Divide the number by 10.
5%
→ Find 10% and divide by 2.
25%
→ Divide the number by 4.
50%
→ Divide the number by 2.
⚠️ 5. Common Mistakes
Mistake 1:
Using the new value instead of
the original value when calculating
percentage increase or decrease.
Mistake 2:
Forgetting to multiply by 100
when calculating percentage.
✍️ 6. Practice Problems
1. Find 25% of 800.
25% of 800
= (25 / 100) × 800
= 200
2. Find 15% of 600.
15% of 600
= (15 / 100) × 600
= 90
3. A number increases
from 400 to 500.
Find the percentage increase.
Increase
= 500 - 400
= 100
Percentage increase
= (100 / 400) × 100
= 25%
4. A price decreases from
₹800 to ₹680.
Find the percentage decrease.
Decrease
= 800 - 680
= 120
Percentage decrease
= (120 / 800) × 100
= 15%
5. 30 is what percentage
of 150?
Percentage
= (30 / 150) × 100
= 20%