Quick Concept Summary
Percentage means "per hundred". In aptitude exams, it appears inside profit and loss, marks, population, salary, elections, mixtures, and data interpretation. The real skill is not the definition; it is converting percentages into easy fractions quickly.
Useful Conversions
| Percentage | Fraction |
|---|---|
| 10% | 1/10 |
| 12.5% | 1/8 |
| 20% | 1/5 |
| 25% | 1/4 |
| 33.33% | 1/3 |
| 50% | 1/2 |
| 75% | 3/4 |
Worked Examples
Example 1: Basic percentage
Find 35% of 480.
35% of 480 = 35/100 × 480 = 168
Example 2: Reverse percentage
After a 20% increase, a salary becomes Rs. 36,000. Find the original salary.
Original = 36,000 × 100 / 120 = 30,000
Example 3: Successive change
A price rises by 10% and then falls by 20%.
Net change = 10 + (-20) + (10 × -20)/100 = -12%
So the final price is 12% lower than the original.
Common Question Types
- Find x% of a number
- Find the original value after percentage change
- Compare two quantities
- Election vote share
- Population increase/decrease
- Marks and pass percentage
Shortcuts
- For
x% of y, sometimes swap:18% of 50 = 50% of 18 = 9 - For equal increase and decrease of
x%, net loss isx^2 / 100 - If a number is reduced by 20%, multiply by
0.8
Practice Questions
1. Find 15% of 640. 2. A number rises from 240 to 300. Find the percentage increase. 3. A population decreases by 10% and then increases by 10%. Find the net change. 4. If 72 is 30% of a number, find the number. 5. A candidate gets 56% of 25,000 votes. How many votes did the opponent get?
Common Mistakes
- Using the changed value as the wrong base
- Treating equal increase and decrease as zero net change
- Forgetting to convert percentage into a fraction or decimal before multiplying
Revision Checklist
- [ ] Fraction conversions memorised
- [ ] Reverse percentage understood
- [ ] Successive-change formula practised
- [ ] Percentage comparison questions revised