📚 Percentages – IBPS Clerk – Quantitative Aptitude
Percent is a way to express a number as a part of 100.
1 % = 1 out of 100 = 0.01 (decimal) = 1/100 (fraction).
1️⃣ Simple Explanation
| Concept | Example | Result |
|---|---|---|
| Percent of a number | 15 % of 200 | (0.15 \times 200 = 30) |
| Percentage increase | Price rises from Rs 200 to Rs 250 | (\frac{250-200}{200} \times 100 = 25%) |
| Percentage decrease | Weight drops from 80 kg to 70 kg | (\frac{80-70}{80} \times 100 = 12.5%) |
| Reverse percentage | 20 % of a number equals 50 | Number = (\frac{50}{0.20} = 250) |
2️⃣ Key Points to Remember
| Point | Why it matters |
|---|---|
| Conversion rule – (x% = \frac{x}{100}) | Converts percentages to decimals or fractions instantly. |
| Multiplication is easier – Calculate percent of a number by multiplying the number with the decimal form. | Faster calculations (e.g., 25 % of 400 → (0.25 \times 400 = 100)). |
| Percentage change – (\frac{\text{New} - \text{Old}}{\text{Old}} \times 100) | Determines how much a value has increased/decreased. |
| Compound percentages – Use successive multiplication: (P \times (1 + r_1)(1 + r_2)\dots) | Handles multiple percentage changes in sequence. |
| Part‑percentage – (\frac{\text{Part}}{\text{Whole}} \times 100) | Finds what percent a part is of the whole. |
| Avoid confusion – “20 % of 100 %” is 20, not 200. | Keeps calculations clean. |
| Mental‑math shortcuts | 10 % = divide by 10, 5 % = divide by 20, 1 % = divide by 100. |
| Check units | Percentages are unit‑less; the base number carries the unit (₹, kg, etc.). |
3️⃣ Core Formulas
| Purpose | Formula | Example |
|---|---|---|
| Percent of a number | (p% \text{ of } N = \frac{p}{100}\times N) | 30 % of 150 → (0.30\times150 = 45) |
| Convert percent to decimal | (d = \frac{p}{100}) | 18 % → 0.18 |
| Percentage increase | (\frac{\text{New}-\text{Old}}{\text{Old}}\times100) | 200 → 250 → 25 % |
| Percentage decrease | (\frac{\text{Old}-\text{New}}{\text{Old}}\times100) | 80 → 70 → 12.5 % |
| Find base from percent & amount | (\text{Base} = \frac{\text{Amount}}{p/100}) | 25 % = 50 → Base = (50/0.25 = 200) |
| Compound percentage | (\text{Final} = \text{Initial}\times(1+r_1)(1+r_2)\dots) | 100 → +10 % → -5 % → 100×1.10×0.95 = 104.5 |
| Part‑percentage | (\frac{\text{Part}}{\text{Whole}}\times100) | 15 of 60 |