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Percentage Change

SBI SO · Quantitative Aptitude

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Core Concept

Read this first — the foundation of the topic

Percentage change is the difference between the original value and the new value, expressed as a percentage of the original value. This concept appears in almost every SSC CGL paper and forms the backbone of profit-loss, simple interest, and data interpretation questions. Core Concept: When any quantity increases or decreases, we calculate the percentage change to measure the rate of change. For example, if your salary increases from Rs 20,000 to Rs 25,000, the percentage increase is 25%. Key

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Formula Block

Memorise — at least one formula appears in every paper

• Percentage Increase = [(New Value - Original Value) / Original Value] × 100

• Percentage Decrease = [(Original Value - New Value) / Original Value] × 100

• New Value after x% increase = Original Value × (100 + x)/100

• New Value after x% decrease = Original Value × (100 - x)/100

• Successive percentage changes: If a value changes by a% then b%, final change = [a + b + (ab/100)]%

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Exam Patterns

What examiners ask — read before attempting PYQs

💡Remember

percentage change is always calculated on the ORIGINAL value, not the new value. If price changes from Rs 100 to Rs 120, the base is Rs 100, not Rs 120. Many students calculate (20/120) × 100 instead of (20/100) × 100, leading to wrong answers

📋Exam Strategy

Practice reverse calculations where you find original values from final values and percentage changes. SSC frequently tests this concept in tricky word problems involving multiple successive changes.

🔑 Key Points

Percentage change = [(New Value - Original Value) / Original Value] × 100
Always use original value as denominator, never the new value
Successive changes formula: a + b + (ab/100) for changes of a% and b%
Quick multipliers: 25% increase = ×1.25, 20% decrease = ×0.8
Two successive changes of x% each = x + x + x²/100 total change
Increase followed by same % decrease gives net decrease of x²/100
12.5% = 1/8, 16.67% = 1/6, 33.33% = 1/3 for quick calculations
Population, salary, price problems are most common question types
Practice finding original values when final value and change% are given
Take original value as 100 for easier calculation in successive changes

📌 Exam Facts

12.5% equals exactly 1/8 fraction
16.67% equals exactly 1/6 fraction
33.33% equals exactly 1/3 fraction
66.67% equals exactly 2/3 fraction
Successive 10% increases give 21% total increase
10% increase followed by 10% decrease gives 1% net decrease
25% increase followed by 20% decrease gives 0% net change
Two successive 50% increases give 125% total increase

🚀 60-Second Revision

Formula: Percentage change = [(New - Original) / Original] × 100
Remember: Original value is always the base for calculation
Successive changes: a + b + (ab/100) for a% then b% change
Trap: Never use new value as denominator in percentage change
Quick trick: Take original as 100 for successive change problems
Memorize: 12.5%=1/8, 16.67%=1/6, 33.33%=1/3, 25%=1/4
Practice: Finding original values from final values and percentages

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