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

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

💡 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:

1. Practice 20-25 questions daily for 1 week
2. Focus on successive percentage and reverse percentage problems
3. Master fraction-percentage conversions for speed

For SSC CHSL:

1. Master basic formulas first
2. Practice 10-15 questions daily
3. Focus on percentage increase/decrease type questions

For SSC MTS:

1. Focus on direct formula-based questions
2. Practice 5-10 basic questions daily
3. Memorize common fraction-percentage conversions

   Practice Percentage

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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

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.

📖 Next Steps

1. Practice Questions: Test your understanding with practice tests
2. Study Materials: Explore comprehensive study resources
3. Daily Quiz: Take today’s quiz