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SSC CGL Preparation – Day 6
Quantitative Aptitude – Percentage
🔹 What is a Percentage?
- The term “percent” means per hundred.
- It is denoted by the symbol %.
- Percentage = (Part / Whole) × 100
🔹 Basic Concepts and Conversions
| Fraction | Percentage |
|---|---|
| 1/2 | 50% |
| 1/3 | 33.33% |
| 1/4 | 25% |
| 1/5 | 20% |
| 1/6 | 16.66% |
| 1/8 | 12.5% |
| 1/10 | 10% |
| 2/3 | 66.66% |
| 3/4 | 75% |
🔹 Important Conversion Tips:
- To convert % to a fraction: Divide by 100 (e.g. 25% = 25/100 = 1/4)
- To convert fraction to %: Multiply by 100 (e.g. 1/4 = 1/4 × 100 = 25%)
🔹 Types of Problems in SSC CGL
1. Finding Percentage of a Number
What is 20% of 150?
Solution:
20% of 150 = (20/100) × 150 = 30
2. Finding What % One Number is of Another
What percent is 40 of 200?
Solution:
(40/200) × 100 = 20%
3. Increase/Decrease Percentage
Increase 250 by 20%
Solution:
20% of 250 = 50
New value = 250 + 50 = 300
Decrease 250 by 20%
250 − 50 = 200
4. Percentage Change
% Change = ((New − Old)/Old) × 100
- Positive value = Increase
- Negative value = Decrease
5. Successive Percentage Change Formula
When a value is increased by x% and then again by y%:
Net % change = x + y + (xy/100)
If one is increase and other decrease:
Net % change = x − y − (xy/100)
🧠 Use only when both %s are applied on the same base.
6. Percentage Comparison / Ratio to %
If A is 25% more than B, then:
- A = B × (1 + 25/100) = B × 1.25
- If A is 25% less than B → A = B × (1 − 25/100) = B × 0.75
🔹 Shortcut Table: Percentage Increase/Decrease
| % Change | Multiplier |
|---|---|
| +10% | × 1.10 |
| −10% | × 0.90 |
| +25% | × 1.25 |
| −25% | × 0.75 |
| +50% | × 1.50 |
| −50% | × 0.50 |
🔹 Application-based Problems
7. Population Problems
Population of a city increases by 10% per year. What will be the population after 2 years if current is 10,000?
Solution:
Year 1 = 10,000 × 1.10 = 11,000
Year 2 = 11,000 × 1.10 = 12,100
8. Exam Marks Type Questions
A student scored 180 marks out of 200. What % did he score?
Answer: (180/200) × 100 = 90%
9. Income & Expenditure / Profit Loss in Terms of %
A man spends 80% of his income. He saves ₹2000. What is his income?
Let income = x
20% of x = 2000 → x = 2000 × 100/20 = ₹10,000
10. Reverse % Problems
If after giving 20% discount, the selling price is ₹400, find the marked price.
Let MP = x
80% of x = 400 → x = 400 × 100/80 = ₹500
🧠 Tips & Tricks
- Remember the base: Always be clear about what the percentage is calculated of.
- Successive change formula helps save time.
- Use fractions for recurring % values (33.33% = 1/3 etc.)
- For comparisons, fix a base value (usually 100) and scale accordingly.
📌 Common Errors to Avoid
- Calculating percentage of the wrong base value.
- Forgetting to apply successive percentage change formula when needed.
- Ignoring the direction of percentage change (increase vs decrease).
