Finding Percentage of a Number
Finding the percentage of a number means calculating what a given percent of a quantity equals. For example, 20% of 150 = 30. This tells us that 20 parts out of every 100 parts of 150 equals 30.
This is one of the most practical maths skills you will ever learn. You use it when calculating discounts while shopping ("20% off ₹500"), figuring out exam marks ("she scored 85% of 200"), computing tips at restaurants, understanding bank interest, and much more.
In Class 5, you will learn to find the percentage of a number using two methods — the fraction method and the decimal method. You will also learn quick mental maths tricks for common percentages like 10%, 25%, and 50%.
Once you master this skill, you will be able to solve discount problems, salary calculations, and data questions with confidence.
What is Finding Percentage of a Number - Class 5 Maths (Percentage)?
Percentage of a number tells you what part of that number a given percentage represents.
"25% of 200" means: if you divide 200 into 100 equal parts, take 25 of those parts. 200 ÷ 100 = 2 (each part), and 25 × 2 = 50. So 25% of 200 = 50.
X% of N = (X / 100) × N
Here, X is the percentage and N is the number. The word "of" in maths means multiplication.
Finding Percentage of a Number Formula
Percentage of a Number = (Percentage ÷ 100) × Number
Method 1: Fraction method
- Write the percentage as a fraction with denominator 100.
- Simplify the fraction if possible.
- Multiply by the number.
Example: 25% of 80 = (25/100) × 80 = (1/4) × 80 = 80 ÷ 4 = 20
Method 2: Decimal method
- Convert the percentage to a decimal (divide by 100).
- Multiply the decimal by the number.
Example: 25% of 80 = 0.25 × 80 = 20
Quick tricks for common percentages (mental maths):
| Percentage | Quick Trick | Example |
|---|---|---|
| 1% | Divide by 100 | 1% of 600 = 6 |
| 5% | Find 10%, then halve it | 5% of 200 = 10 |
| 10% | Divide by 10 | 10% of 350 = 35 |
| 20% | Divide by 5 | 20% of 250 = 50 |
| 25% | Divide by 4 | 25% of 120 = 30 |
| 50% | Divide by 2 | 50% of 84 = 42 |
| 75% | Find 50% + 25% | 75% of 80 = 40+20 = 60 |
These tricks make calculations faster and are especially useful in exams and daily life.
Types and Properties
Type 1: Percentage of a whole number
Find 30% of 200. → (30/100) × 200 = 60.
Type 2: Percentage of a decimal number
Find 50% of 12.6. → (50/100) × 12.6 = 0.5 × 12.6 = 6.3.
Type 3: Percentage of money (₹)
Find 15% of ₹400. → (15/100) × 400 = ₹60.
Type 4: Percentage of a measurement
Find 20% of 5 kg. → (20/100) × 5 = 1 kg.
Type 5: Non-standard percentages
Find 33% of 300. → (33/100) × 300 = 99.
Find 12.5% of 640. → (12.5/100) × 640 = 0.125 × 640 = 80.
Solved Examples
Example 1: Finding 10% Using the Quick Trick
Problem: Find 10% of 250.
Solution:
Step 1: To find 10%, divide the number by 10.
Step 2: 250 ÷ 10 = 25
Why this works: 10% = 10/100 = 1/10. Taking 1/10 of a number means dividing by 10.
Answer: 10% of 250 = 25
Example 2: Finding 25% Using the Quick Trick
Problem: Find 25% of 360.
Solution:
Step 1: To find 25%, divide the number by 4.
Step 2: 360 ÷ 4 = 90
Why this works: 25% = 25/100 = 1/4. Taking 1/4 of a number means dividing by 4.
Answer: 25% of 360 = 90
Example 3: Finding 50% — Half
Problem: Find 50% of 84.
Solution:
Step 1: 50% means half. Divide by 2.
Step 2: 84 ÷ 2 = 42
Answer: 50% of 84 = 42
Example 4: Word Problem — Shopping Discount
Problem: A school bag costs ₹600. The shop gives a 20% discount. How much is the discount? What is the sale price?
Solution:
Step 1: Discount amount = 20% of ₹600
Step 2: 20/100 × 600 = 1/5 × 600 = ₹120
Step 3: Sale price = ₹600 − ₹120 = ₹480
Answer: The discount is ₹120 and the sale price is ₹480.
Example 5: Word Problem — Exam Marks
Problem: Priya scored 80% in an exam with a maximum of 50 marks. How many marks did she score?
Solution:
Step 1: Marks = 80% of 50
Step 2: (80/100) × 50 = 4/5 × 50 = 40
Verification: 40 out of 50 = 40/50 = 80% ✓
Answer: Priya scored 40 marks.
Example 6: Finding 15% Using the Building-Up Method
Problem: Find 15% of 200.
Solution:
Step 1: Break 15% into 10% + 5%.
Step 2: 10% of 200 = 200 ÷ 10 = 20
Step 3: 5% of 200 = half of 10% = 20 ÷ 2 = 10
Step 4: 15% = 20 + 10 = 30
Why this method works: You can build any percentage from combinations of 10%, 5%, and 1%. This is extremely useful for mental maths.
Answer: 15% of 200 = 30
Example 7: Word Problem — Monthly Savings
Problem: Aman's father earns ₹5,000 per month and saves 30% of his income. How much does he save? How much does he spend?
Solution:
Step 1: Savings = 30% of ₹5,000 = (30/100) × 5,000 = 3/10 × 5,000 = ₹1,500
Step 2: Amount spent = ₹5,000 − ₹1,500 = ₹3,500
Alternatively: Spending = 100% − 30% = 70% of ₹5,000 = ₹3,500.
Answer: He saves ₹1,500 and spends ₹3,500 per month.
Example 8: Finding 75% of a Number
Problem: Find 75% of 480.
Solution:
Step 1: 75% = 3/4.
Step 2: 3/4 × 480 = (480 ÷ 4) × 3 = 120 × 3 = 360
Alternative (building up): 50% of 480 = 240. 25% of 480 = 120. 75% = 240 + 120 = 360. ✓
Answer: 75% of 480 = 360
Example 9: Word Problem — School Attendance
Problem: A school has 800 students. On Monday, 95% were present. How many students were present? How many were absent?
Solution:
Step 1: Present = 95% of 800 = (95/100) × 800
Step 2: 95 × 800 ÷ 100 = 95 × 8 = 760
Step 3: Absent = 800 − 760 = 40 students.
Alternative: Absent = 5% of 800 = (5/100) × 800 = 40. ✓
Answer: 760 students were present and 40 students were absent.
Example 10: Finding 1% — The Foundation
Problem: Find 1% of 4,500.
Solution:
Step 1: 1% = 1/100. To find 1%, divide by 100.
Step 2: 4,500 ÷ 100 = 45
Why 1% is useful: Once you know 1%, you can find any percentage by multiplication. For example, 3% of 4,500 = 3 × 45 = 135. And 7% of 4,500 = 7 × 45 = 315.
Answer: 1% of 4,500 = 45
Real-World Applications
Where do we find percentage of a number in daily life?
- Shopping discounts: A 25% discount on a ₹1,200 dress means you save (25/100) × 1,200 = ₹300. You pay ₹900.
- Exam scores: If a student scores 85% in a 200-mark exam, they got (85/100) × 200 = 170 marks.
- Tips at restaurants: A 10% tip on a ₹500 bill = ₹50.
- Bank interest: 5% interest on a ₹10,000 fixed deposit gives ₹500 per year.
- Nutrition labels: If a cereal box says 12% protein per 100 g serving, a 50 g serving has 6 g protein.
- Taxes: GST of 18% on a ₹1,000 item means ₹180 tax, total ₹1,180.
- Sports: If a team wins 60% of 20 matches, they won 12 matches.
Key Points to Remember
- Percentage of a number = (Percentage ÷ 100) × Number.
- The word "of" in "25% of 80" means multiplication.
- Quick tricks: 10% = ÷10. 50% = ÷2. 25% = ÷4. 1% = ÷100. 20% = ÷5.
- For 15%, find 10% and 5% separately and add. For 75%, find 50% and 25% and add.
- 100% of any number equals the number itself. 0% of any number is 0.
- More than 100% gives a result larger than the original number (e.g., 200% of 50 = 100).
- Always include the correct unit in your answer (₹, marks, students, kg, etc.).
- Verify your answer: if 20% of 500 = 100, check that 100 is one-fifth of 500 ✓.
Practice Problems
- Find 20% of 450.
- Ria scored 75% in a test of 80 marks. How many marks did she score?
- A shopkeeper gives a 10% discount on an item priced at ₹850. What is the discount amount and the selling price?
- Find 5% of 1,200.
- A train has 500 seats. If 60% are occupied, how many seats are occupied and how many are empty?
- Calculate 33% of 300.
- Dev's monthly pocket money is ₹2,000. He spends 45% on books and stationery. How much does he spend?
- Find 12.5% of 640.
Frequently Asked Questions
Q1. How do you find the percentage of a number?
Divide the percentage by 100 and multiply by the number. For example, 30% of 200 = (30/100) × 200 = 60. You can also convert the percentage to a decimal first: 30% = 0.30, then 0.30 × 200 = 60.
Q2. What is the fastest way to find 10% of a number?
Divide the number by 10. For example, 10% of 350 = 350 ÷ 10 = 35. This works because 10% = 1/10.
Q3. How do you find 25% of a number?
Divide the number by 4. For example, 25% of 200 = 200 ÷ 4 = 50. This works because 25% = 1/4 = one quarter.
Q4. What is 100% of any number?
100% of any number is the number itself. For example, 100% of 75 = 75. This is because 100/100 = 1, and multiplying by 1 does not change the number.
Q5. How do you find 15% of a number quickly?
Find 10% first (divide by 10), then find 5% (halve the 10% result), and add them together. For example, 15% of 400: 10% = 40, 5% = 20, so 15% = 40 + 20 = 60.
Q6. Can the percentage of a number be larger than the number itself?
Yes, when the percentage is more than 100%. For example, 200% of 50 = (200/100) × 50 = 2 × 50 = 100, which is larger than 50. This happens with price increases, growth calculations, etc.
Q7. What is the difference between 'finding a percentage' and 'finding the percentage of a number'?
Finding a percentage means calculating what percent one number is of another (e.g., 30 is what % of 150? Answer: 20%). Finding the percentage of a number means calculating a given percent of a quantity (e.g., what is 60% of 150? Answer: 90). They are related but different questions.
Q8. How is finding percentage of a number useful in shopping?
When a shop offers a 20% discount on a ₹500 item, you calculate 20% of 500 = ₹100 as the discount. The sale price becomes ₹500 − ₹100 = ₹400. This helps you know exactly how much you save and pay.
