Percentages – Quick & Easy Study Notes
(Manipur PSC – Quantitative Aptitude)
1. What is a Percent?
- Percent means “out of 100.”
- Think of a pizza cut into 100 equal slices.
- 10 slices → 10 % of the pizza.
- 25 slices → 25 % of the pizza.
Very short rule
percent = (part ÷ whole) × 100
2. How to Find a Percent of a Number
- Write the percent as a decimal.
- 30 % → 0.30
- Multiply the decimal by the number.
| Percent | Decimal | Example | Result |
|---|---|---|---|
| 30 % | 0.30 | 0.30 × 200 | 60 |
| 12 % | 0.12 | 0.12 × 75 | 9 |
Tiny Example
What is 15 % of 80?
- 15 % → 0.15
- 0.15 × 80 = 12
3. How to Find What Percent One Number Is of Another
Use the reverse of the rule above.
percent = (part ÷ whole) × 100
| Part | Whole | Formula | Result |
|---|---|---|---|
| 45 | 150 | (45 ÷ 150) × 100 | 30 % |
| 25 | 200 | (25 ÷ 200) × 100 | 12.5 % |
Tiny Example
120 is what percent of 400?
- 120 ÷ 400 = 0.30
- 0.30 × 100 = 30 %
4. Increase or Decrease by a Percent
- Increase:
new = old + (increase% of old) - Decrease:
new = old - (decrease% of old)
| Action | Formula | Tiny Example |
|---|---|---|
| +10 % to 200 | 200 + 0.10 × 200 = 200 + 20 | 220 |
| –25 % from 80 | 80 – 0.25 × 80 = 80 – 20 | 60 |
5. Percent of a Percent (Nested Percent)
Multiply the decimals.
(a % of b % of X) = (a/100) × (b/100) × X
| a % | b % | X | Result |
|---|---|---|---|
| 20 % | 30 % | 500 | (0.20 × 0.30 × 500) = 30 |
Tiny Example
25 % of 40 % of 200
- 0.25 × 0.40 × 200 = 20
6. Quick Mental Tricks
| Trick | When to Use | Example |
|---|---|---|
| 10 % is just one‑tenth | Quick check | 10 % of 120 = 12 |
| Double for 20 % | 20 % = 10 % × 2 | 20 % of 250 = 25 × 2 = 50 |
| Subtract 10 % then add 1 % | 9 % = 10 % – 1 % | 9 % of 300 = 30 – 3 = 27 |
| Add 5 % = half of 10 % | 5 % = 10 % ÷ 2 | 5 % of 800 = 80 ÷ 2 = 40 |
7. Quick Reference Table
| What to Find | Formula (simple) | Quick Mental Hint |
|---|---|---|
| Percent of a number | number × percent ÷ 100 |
Think “slice” of the number |
| Number that is a percent of another | whole × percent ÷ 100 |
Reverse of above |
| New number after percent increase | old + (old × percent ÷ 100) |
“Add a slice” |
| New number after percent decrease | old – (old × percent ÷ 100) |
“Remove a slice” |
8. Practice Questions (Answer in the last column)
| # | Question | Answer |
|---|---|---|
| 1 | 25 % of 160 | 40 |
| 2 | 60 is what percent of 200? | 30 % |
| 3 | A price increases by 15 % from 200 to? | 230 |
| 4 | A price decreases by 20 % from 350 to? | 280 |
| 5 | 12 % of 12 % of 240 | 34.56 |
| 6 | 18 % of 75 is how many? | 13.5 |
| 7 | 50 is what percent of X if X = 200? | 25 % |