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Basic Percentage

UP Police Constable · Quantitative Aptitude

Also prepare for:CRPF Const BSF Const CISF Const ITBP Const

Percentage Change →

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Core Concept

Read this first — the foundation of the topic

→Core Concept

Percentage is a way to express a fraction with denominator 100. When you say 25%, it means 25 out of 100 parts. Think of it as cutting a pie into 100 equal slices and taking some of them

💡Key Rules and Properties

First, percentage is always calculated on a base value. Second, 100% means the complete quantity. Third, percentages can exceed 100% when the part is larger than the whole. Fourth, percentage change and percentage of a number are different concepts

🔑Essential Formulas

• Percentage = (Part/Whole) × 100 • Part = (Percentage/100) × Whole • Whole = (Part × 100)/Percentage • Percentage to Fraction: x% = x/100 • Percentage to Decimal: x% = x/100 = 0.0x

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Exam Patterns

What examiners ask — read before attempting PYQs

⚡Powerful Shortcuts for Quick Calculation

Shortcut 1 - Common Percentage Conversions: • 50% = 1/2, 25% = 1/4, 20% = 1/5, 10% = 1/10 • 33.33% = 1/3, 66.67% = 2/3, 12.5% = 1/8, 16.67% = 1/6 Memorize these to solve faster without calculations

⚡Shortcut 2 - Quick Mental Math Trick

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Convert percentage to decimal: 24% = 24/100 = 0.24

2

Multiply: 850 × 0.24

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Break it down: 850 × 0.24 = 850 × (20/100 + 4/100)

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Calculate: 850 × 0.20 = 170, and 850 × 0.04 = 34

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Add: 170 + 34 = 204 Answer: 24% of 850 = 204 Worked Example 2: What percentage is 156 of 240?

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Use formula: Percentage = (Part/Whole) × 100

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Substitute values: (156/240) × 100

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Simplify fraction: 156/240 = 13/20 (dividing by 12)

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Convert to decimal: 13/20 = 0.65

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Multiply by 100: 0.65 × 100 = 65% Answer: 156 is 65% of 240 Shortcut 3 - The Unitary Method for Percentages: If x% = y, then 1% = y/x, and 100% = (y × 100)/x This eliminates complex calculations in competitive exams. Common Mistake - The #1 Trap: Students confuse 'percentage of' with 'percentage more than'. For example, if A is 20% of B, it does NOT mean A is 20% more than B. '20% of B' means A = 0.20 × B. But '20% more than B' means A = B + 0.20 × B = 1.20 × B. This confusion costs precious marks in exams. Another frequent error is forgetting to convert percentage back to the required form. Always check if the answer needs to be in percentage, decimal, or fraction format.

🔑 Key Points

Percentage means parts per hundred, always calculated on a base value
Quick conversion: 50% = 1/2, 25% = 1/4, 20% = 1/5, 10% = 1/10
Formula: Percentage = (Part/Whole) × 100
Memorize: 33.33% = 1/3, 66.67% = 2/3, 12.5% = 1/8
To find x% of a number, multiply the number by x/100
Shortcut: Break complex percentages into easier chunks (15% = 10% + 5%)
Part = (Percentage/100) × Whole gives the actual quantity
Whole = (Part × 100)/Percentage when base value is unknown
Never confuse 'percentage of' with 'percentage more than'
Always check if final answer needs percentage, decimal, or fraction form

📌 Exam Facts

100% represents the complete quantity or whole
0.5% equals 1/200 in fractional form
Percentage formula: (Part/Whole) × 100
12.5% conversion: 12.5/100 = 1/8
16.67% (rounded) equals exactly 1/6
37.5% equals 3/8 in simplest fraction form
To convert percentage to decimal: divide by 100
87.5% equals 7/8 when expressed as a fraction

🚀 60-Second Revision

Remember: Percentage = (Part/Whole) × 100 for all basic problems
Formula: Part = (Percentage/100) × Whole for finding quantities
Trap: 'x% of y' ≠ 'x% more than y' - completely different meanings
Shortcut: Use fraction conversions (25% = 1/4) for faster calculations
Quick check: 50% should always give exactly half the original number
Mental math: Break percentages (15% = 10% + 5%) for speed
Always verify if answer format should be percentage, decimal, or fraction

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