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Agniveer Army CEE Percentage Change

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This page covers Agniveer Army CEE Percentage Change with complete concept notes, 8 graded practice MCQs, key points and exam-specific tips. Free to study.

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Concept Notes

Percentage Change— Rules & Concept

Core ConceptRead 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%.

Formula BlockMemorise — at least one formula appears in every paper

Block:

• 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)]%
Exam PatternsWhat examiners ask — read before attempting PYQs

SSC loves asking percentage change in population growth, salary hikes, price fluctuations, and successive discounts. Questions often involve finding original values when final values and percentage changes are given.

ShortcutsUse these to save 30–60 seconds per question
1

Two successive increases of x% = (x + x + x²/100)% total increase

2

One increase of x% followed by decrease of x% = (x²/100)% net decrease

3

25% increase means multiply by 1.25

4

20% decrease means multiply by 0.8

5

12.5% increase means multiply by 9/8

Worked ExampleSolve this step-by-step before moving on
1
Step 1

Identify original value = 50,000, new value = 65,000

2
Step 2

Find increase = 65,000 - 50,000 = 15,000

3
Step 3

Apply formula = (15,000/50,000) × 100 = 30% Answer: 30% increase Worked Example 2: A number is first increased by 20% and then decreased by 15%. Find the overall percentage change.

1
Step 1

Let original number = 100 (always take 100 for easier calculation)

2
Step 2

After 20% increase = 100 × 1.2 = 120

3
Step 3

After 15% decrease = 120 × 0.85 = 102

4
Step 4

Overall change = 102 - 100 = 2

5
Step 5

Percentage change = 2% increase Alternative: Using formula = 20 + (-15) + (20×(-15)/100) = 20 - 15 - 3 = 2% increase Shortcut Trick #3: Percentage to fraction conversions: • 12.5% = 1/8, 16.67% = 1/6, 33.33% = 1/3, 66.67% = 2/3 • These help in quick mental calculations during exams.

Exam TrapsCommon mistakes students make — avoid these

#1: Students often confuse which value to use as base. 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 to Remember

  • 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-Specific Tips

  • 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
Practice MCQs

Percentage Change — Practice Questions

8graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1easy

The price of a book increased from ₹200 to ₹250. What is the percentage increase in price?

Practice 2easy

A student scored 60 marks out of 100 in an exam. In the next exam, the marks increased to 75 out of 100. What is the percentage increase in marks?

Practice 3easy

The population of a town decreased from 5000 to 4500 in one year. What is the percentage decrease in population?

Practice 4medium

A shopkeeper reduced the price of a shirt from ₹800 to ₹600. What is the percentage decrease in price?

Practice 5medium

The population of a village decreased from 5000 to 4500 in one year. What is the percentage decrease in population?

Practice 6medium

A student scored 45 marks in an exam. After revision, the score increased to 54 marks. What is the percentage increase in marks?

Practice 7medium

The price of a book was ₹240. It was increased to ₹300. What is the percentage increase in price?

Practice 8hard

The price of a laptop was ₹50,000 in 2022. In 2023, the price increased by 20%. In 2024, the price decreased by 10% from the 2023 price. What is the overall percentage change in the price from 2022 to 2024?

60-Second Revision — Percentage Change

  • 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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