Percentage - Complete Guide for SSC Exams
Prerequisites
Before studying this topic, make sure you understand:
What is Percentage?
Percentage means “per hundred” or “out of 100”. It is denoted by the symbol %.
When we say 25%, it means 25 out of 100 or 25/100 or 0.25 as a decimal.
Why Percentage is Important for SSC?
- ✅ Asked in every SSC exam without fail
- ✅ Foundation for Profit/Loss, SI/CI, Discount topics
- ✅ Easy to score if you know the formulas
- ✅ Questions can be solved in 30-45 seconds with tricks
Important Formulas
1. Basic Conversion Formulas
Concept | Formula |
---|---|
Fraction to Percentage | (Fraction × 100)% |
Percentage to Fraction | Percentage/100 |
Decimal to Percentage | (Decimal × 100)% |
Percentage to Decimal | Percentage/100 |
2. Percentage Calculation Formulas
Percentage = (Value/Total Value) × 100%
Value = (Percentage/100) × Total Value
Total Value = (Value × 100)/Percentage
3. Percentage Increase/Decrease
Percentage Increase = [(New Value - Original Value)/Original Value] × 100%
Percentage Decrease = [(Original Value - New Value)/Original Value] × 100%
New Value after Increase = Original × (100 + Increase%)/100
New Value after Decrease = Original × (100 - Decrease%)/100
4. Successive Percentage Changes
When two percentage changes are applied successively:
Net Change = a + b + (ab/100)
Where a and b are the percentage changes (use negative sign for decrease)
5. Common Fraction-Percentage Conversions
Fraction | Percentage | Fraction | Percentage |
---|---|---|---|
1/2 | 50% | 1/3 | 33.33% |
1/4 | 25% | 3/4 | 75% |
1/5 | 20% | 2/5 | 40% |
1/8 | 12.5% | 3/8 | 37.5% |
1/10 | 10% | 1/6 | 16.66% |
💡 Pro Tip: Memorize these conversions! They save 10-15 seconds per question.
Solved Examples
Example 1: Basic Percentage Calculation
Question: What is 25% of 640?
Solution:
25% of 640 = (25/100) × 640
= (1/4) × 640
= 160
Answer: 160
Example 2: Percentage Increase
Question: The price of a shirt increases from ₹500 to ₹650. Find the percentage increase.
Solution:
Increase = 650 - 500 = ₹150
Percentage Increase = (150/500) × 100%
= 30%
Answer: 30%
Example 3: Successive Percentage Changes
Question: The population of a city increases by 10% in the first year and 20% in the second year. Find the net percentage increase.
Solution:
Using formula: Net Change = a + b + (ab/100)
= 10 + 20 + (10 × 20)/100
= 30 + 200/100
= 30 + 2
= 32%
Answer: 32%
Example 4: Reverse Percentage (SSC Favorite!)
Question: If 15% of a number is 45, find the number.
Solution:
Let the number be x
15% of x = 45
(15/100) × x = 45
x = (45 × 100)/15
x = 300
Answer: 300
Important Shortcuts & Tricks
Trick 1: Quick Percentage Calculation
To find 12.5% of any number: Divide by 8
To find 16.66% of any number: Divide by 6
To find 33.33% of any number: Divide by 3
Trick 2: Percentage Increase/Decrease
If a value is increased by x% and then decreased by x%, there is always a net decrease.
Net Decrease = (x²/100)%
Example: Increase by 20%, then decrease by 20% → Net decrease = (20²/100)% = 4%
Trick 3: Comparing Percentages
To compare a% of b vs b% of a → They are always equal!
20% of 50 = 50% of 20 = 10
Common Mistakes to Avoid
❌ Mistake 1: Confusing percentage increase with final value
- Correct: If 100 increases by 20%, new value = 120, not 20
❌ Mistake 2: Adding percentages directly in successive changes
- Wrong: 10% + 20% = 30%
- Correct: Use formula → 10 + 20 + (10×20)/100 = 32%
❌ Mistake 3: Using wrong base for percentage calculation
- Always use original value as base, not the new value
Practice Strategy for SSC
For SSC CGL:
- Practice 20-25 questions daily for 1 week
- Focus on successive percentage and reverse percentage problems
- Master fraction-percentage conversions for speed
For SSC CHSL:
- Master basic formulas first
- Practice 10-15 questions daily
- Focus on percentage increase/decrease type questions
For SSC MTS:
- Focus on direct formula-based questions
- Practice 5-10 basic questions daily
- Memorize common fraction-percentage conversions
Related Topics to Study Next
Students who master Percentage should also study these closely related topics:
Exam-Specific Previous Year Trends
SSC CGL Analysis
- 2024: 9 questions, mostly successive percentage
- 2023: 10 questions, reverse percentage common
- Difficulty: Easy to Moderate
Practice SSC CGL Percentage Questions →
SSC CHSL Analysis
- Expected Questions: 5-7 per exam
- Common Types: Basic calculations, increase/decrease
- Time Required: 30-45 seconds per question
💡 Study Tip: Percentage is the foundation topic. Master this before moving to Profit and Loss or Simple Interest.