PERCENTAGE

Percentage is one of the most frequently used concepts in CSAT. Though questions may appear simple, they often involve hidden traps related to comparison, successive change, or incorrect base value. A clear conceptual understanding of percentage is essential because it forms the base for Profit–Loss, Simple & Compound Interest, Data Interpretation, and Ratio–Proportion.

MEANING OF PERCENTAGE

• The word ‘percent’ means “per hundred”
• Percentage represents a fraction out of 100

Example:
• 25 percent means 25 out of 100
• 25 percent = 25/100 = 0.25

BASIC PERCENTAGE CONVERSIONS

Fraction to Percentage
• Multiply the fraction by 100
• Example: 3/4 = 75 percent

Decimal to Percentage
• Multiply by 100
• Example: 0.2 = 20 percent

Percentage to Fraction
• Divide by 100
• Example: 40 percent = 40/100 = 2/5

FINDING PERCENTAGE OF A NUMBER

Formula
• Percentage of a number = (Percentage × Number) / 100

Example
• 20 percent of 150 = (20 × 150) / 100 = 30

CSAT Tip
• Use fraction equivalents:
  – 25 percent = 1/4
  – 50 percent = 1/2
  – 10 percent = 1/10

PERCENTAGE INCREASE AND DECREASE

Increase
• New Value = Original Value + Increase
• Percentage Increase = (Increase / Original Value) × 100

Decrease
• New Value = Original Value − Decrease
• Percentage Decrease = (Decrease / Original Value) × 100

Important Concept
• Percentage change is always calculated on the original value

SUCCESSIVE PERCENTAGE CHANGE

When two or more percentage changes occur one after another, they are called successive changes.

Formula
• Net percentage change = a + b + (ab / 100)
Where:
• a and b are percentage changes
• Use negative sign for decrease

Example
• 10 percent increase followed by 10 percent decrease
• Net change = 10 − 10 − (100/100) = −1 percent
• Result is a loss of 1 percent

PERCENTAGE COMPARISON

• Used to compare two quantities with different bases

Example
• Increase from 50 to 60 = 20 percent increase
• Decrease from 60 to 50 = 16.67 percent decrease

PERCENTAGE AND RATIO RELATION

• Percentage can be converted into ratio and vice versa

Example
• 25 percent = 25:100 = 1:4
• Ratio 2:5 = (2/5) × 100 = 40 percent

COMMON PERCENTAGE VALUES (MUST REMEMBER)

• 1/2 = 50 percent
• 1/3 = 33.33 percent
• 1/4 = 25 percent
• 1/5 = 20 percent
• 2/3 = 66.67 percent
• 3/4 = 75 percent

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Subject: CSAT

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