📊 Percentages – Quick & Easy Notes
(For Delhi Patwari / Lekhpal – Quantitative Aptitude)
Percent = “per hundred.”
Think of a whole cake divided into 100 equal slices.
If you take 30 slices, you have 30 % of the cake.
1. Basic Idea
| Term | What it means | Everyday picture |
|---|---|---|
| Whole | The total amount you’re looking at | 100 % of the cake |
| Part | The section you’re interested in | 30 slices of the cake |
| Percent | “Part of 100.” | 30 slices out of 100 → 30 % |
2. Simple Percent Calculation
Formula
Percent = (Part ÷ Whole) × 100
Example
- Whole = 80 sq ft (land area)
- Part = 12 sq ft (taxable portion)
Percent = (12 ÷ 80) × 100
= 0.15 × 100
= 15%
So 15 % of the land is taxable.
3. From Fraction / Decimal to Percent
| Fraction | Decimal | Percent |
|---|---|---|
| 1/4 | 0.25 | 25 % |
| 3/5 | 0.60 | 60 % |
| 7/10 | 0.70 | 70 % |
Rule – Multiply the decimal by 100 and add “%”.
4. From Percent to Fraction / Decimal
| Percent | Decimal | Fraction (simplest) |
|---|---|---|
| 25 % | 0.25 | 1/4 |
| 60 % | 0.60 | 3/5 |
| 70 % | 0.70 | 7/10 |
Rule – Divide by 100 or move the decimal two places left.
5. “What Percent of X?” – Finding the Part
Formula
Part = (Percent × Whole) ÷ 100
Example
- Whole land = 200 sq ft
- Percent taxable = 12 %
Part = (12 × 200) ÷ 100
= 2400 ÷ 100
= 24 sq ft
So 24 sq ft of the land is taxable.
6. Percentage Increase / Decrease
| Situation | Formula | Quick Check |
|---|---|---|
| Increase | New = Old × (1 + Percent/100) |
Add the percent to 100 % |
| Decrease | New = Old × (1 – Percent/100) |
Subtract the percent from 100 % |
Example – Increase
- Old tax rate = 5 %
- Increase = 2 %
New rate = 5 × (1 + 2/100)
= 5 × 1.02
= 5.1 %
Example – Decrease
- Old fee = ₹1000
- Decrease = 15 %
New fee = 1000 × (1 – 15/100)
= 1000 × 0.85
= ₹850
7. Quick Reference Sheet
| What to do | How |
|---|---|
| Find percent of a number | (part ÷ whole) × 100 |
| Find part when percent known | (percent × whole) ÷ 100 |
| Convert fraction → percent | multiply by 100 |
| Convert percent → fraction | divide by 100, simplify |
8. Mini‑Practice Problems
| # | Question | Answer |
|---|---|---|
| 1 | 25 % of 120 sq ft? | 30 sq ft |
| 2 | 40 % of 250 sq ft? | 100 sq ft |
| 3 | 15 % of 200 sq ft? | 30 sq ft |
| 4 | How many percent is 18 out of 60? | 30 % |
| 5 | 80 sq ft is 20 % of what total? | 400 sq ft |
| 6 | Increase ₹500 by 10 %? | ₹550 |
| 7 | Decrease ₹800 by 25 %? | ₹600 |
9. Everyday Tips
- Visualise – Think of a pie chart or a 100‑slice cake.
- Round first – If numbers are messy, round to nearest 10 or 5 before multiplying.
- Check units – If you deal with area (sq ft), keep the units the same on both sides of the equation.
Bottom line
Percentages are just a way to talk about “part of 100.”
Use the simple “multiply by 100” or “divide by 100” tricks, and you’ll handle all land‑related calculations with confidence.