- Percentage = (Part ÷ Whole) × 100.
- To find X% of a number, multiply by X and divide by 100.
- Percentage change = (New − Old) ÷ Old × 100.
- To remove GST from a price, divide by (1 + rate ÷ 100), not subtract.
- Percentage increases compound, so they do not simply add up.
Percentages appear everywhere in daily life in India: exam results, sale offers, loan rates, salary hikes and GST bills. Once you understand three basic formulas, you can solve almost any percentage question.
The basic formula
Percentage = (Part ÷ Whole) × 100
Example: you answered 45 out of 60 questions correctly. 45 ÷ 60 × 100 = 75%.
1. Marks percentage
Add your marks in all subjects, divide by the total maximum marks, and multiply by 100.
Example: 432 out of 500 = 432 ÷ 500 × 100 = 86.4%.
For CGPA, CBSE’s commonly used indicative conversion is CGPA × 9.5. Other boards and universities have their own rules, so check your marksheet.
2. Finding X% of a number
X% of Y = Y × X ÷ 100
Example: 18% of ₹2,500 = 2,500 × 18 ÷ 100 = ₹450.
3. Discount and sale price
A shirt costs ₹1,200 with 25% off. Discount = 1,200 × 25 ÷ 100 = ₹300, so you pay ₹900.
Two discounts do not add up. 20% off followed by an extra 10% off equals 28% off, not 30%, because the second discount applies to the already reduced price.
4. Percentage increase and decrease
% change = (New − Old) ÷ Old × 100
- Salary from ₹25,000 to ₹30,000: (30,000 − 25,000) ÷ 25,000 × 100 = 20% increase.
- Price from ₹500 to ₹400: (400 − 500) ÷ 500 × 100 = 20% decrease.
5. Profit percentage and margin
Cost ₹600, selling price ₹1,000, profit ₹400.
- Profit on cost (markup): 400 ÷ 600 × 100 = 66.7%.
- Profit margin on selling price: 400 ÷ 1,000 × 100 = 40%.
Businesses often confuse these. Use our profit margin calculator to check.
6. GST: adding and removing
- Adding 18% GST to ₹10,000: 10,000 × 1.18 = ₹11,800.
- Removing 18% GST from ₹11,800: 11,800 ÷ 1.18 = ₹10,000.
Subtracting 18% of ₹11,800 gives ₹9,676, which is wrong. Use the GST calculator for any rate.
7. Growth over several years
Sales growing 10% every year for 3 years is not 30%. It is 1.1 × 1.1 × 1.1 = 1.331, or 33.1%. This compounding is why long-term savings grow faster over time.
Mental maths shortcuts
- 10% → divide by 10.
- 5% → half of 10%.
- 25% → divide by 4.
- X% of Y = Y% of X, so 8% of 50 = 50% of 8 = 4.
Do it instantly
8. Percentages in exams with negative marking
Suppose a test has 100 questions, with +4 for a correct answer and −1 for a wrong one. You attempt 80 questions and get 60 right and 20 wrong.
- Score = (60 × 4) − (20 × 1) = 240 − 20 = 220
- Maximum = 100 × 4 = 400
- Percentage = 220 ÷ 400 × 100 = 55%
9. Monthly interest rates
Loans and credit cards sometimes quote a monthly rate. A 2% monthly rate is not the same as 24% a year once compounding is included: 1.02 to the power 12 is about 1.268, or roughly 26.8% a year. Always compare loans using the annual rate.
10. GST included in a price
If a bill shows ₹5,900 including 18% GST, the GST part is 5,900 − (5,900 ÷ 1.18) = 5,900 − 5,000 = ₹900.
Common percentage mistakes
- Adding percentage changes: a 50% rise followed by a 50% fall leaves you at 75% of where you started, not back at 100%.
- Using the wrong base: percentage change is always calculated on the old value.
- Confusing percent and percentage points: 8% to 9% is a 1 percentage point rise, but a 12.5% increase.
- Removing GST by subtracting: always divide by (1 + rate ÷ 100).
Practice questions (with answers)
- What is 15% of ₹3,200? Answer: ₹480.
- You scored 342 out of 450. What is your percentage? Answer: 76%.
- A phone falls from ₹20,000 to ₹17,000. What is the percentage decrease? Answer: 15%.
- You paid ₹1,600 after a 20% discount. What was the original price? Answer: ₹2,000.
Our free percentage calculator solves all of these, with seven calculators on one page that update as you type.
