Percentage

1. Meaning of Percentage

PERCENTAGE means 'per hundred' or 'out of 100'. The symbol % is used to denote percentage.

35% means 35 out of 100 = 35/100 = 0.35.

Why Percentage?

• Makes comparison EASY (common base of 100).
• Used in discounts, interest rates, test scores, population data, etc.
• Standard way to express ratios in daily life.

2. Conversions Between Forms

Fraction to Percentage

Multiply the fraction by 100%.

Examples:

• 3/5 = (3/5 × 100)% = 60%
• 7/20 = (7/20 × 100)% = 35%
• 1/3 = (1/3 × 100)% = 33 1/3% or 33.33%

Decimal to Percentage

Multiply the decimal by 100%.

Examples:

• 0.45 = 0.45 × 100% = 45%
• 0.075 = 0.075 × 100% = 7.5%
• 1.25 = 1.25 × 100% = 125%

Percentage to Fraction

Divide by 100% and simplify.

Examples:

• 60% = 60/100 = 3/5
• 12.5% = 12.5/100 = 125/1000 = 1/8
• 33 1/3% = (100/3)/100 = 100/300 = 1/3

Percentage to Decimal

Divide by 100.

Examples:

• 45% = 45/100 = 0.45
• 125% = 125/100 = 1.25

3. Finding Percentage of a Quantity

Formula

Percentage of a quantity = (Percentage/100) × Quantity

Worked Examples

Example 1: Find 15% of ₹200. 15% of 200 = (15/100) × 200 = ₹30.

Example 2: What percent of 80 is 20? (20/80) × 100% = 25%.

Example 3: If 30% of a number is 45, find the number. Let number be x. 30% of x = 45. (30/100)x = 45. x = 45 × 100/30 = 150.

4. Expressing One Quantity as Percentage of Another

Formula

(First quantity / Second quantity) × 100%

Example (ICSE 2024, 2 marks): 'In a class of 50 students, 18 are girls. What percentage are boys?' Boys = 50 - 18 = 32. Percentage of boys = (32/50) × 100% = 64%.

Comparison Using Percentage

'Which is larger: 3 out of 5 or 5 out of 8?' 3/5 = 60%. 5/8 = 62.5%. 5 out of 8 is larger.

5. Percentage Increase and Decrease

Percentage Increase

% Increase = (Increase in value / Original value) × 100%

Example (ICSE 2023, 3 marks): 'The population of a town increased from 40,000 to 46,000. Find the percentage increase.' Increase = 46,000 - 40,000 = 6,000. % Increase = (6,000/40,000) × 100% = 15%.

Percentage Decrease

% Decrease = (Decrease in value / Original value) × 100%

Example: 'A shirt costing ₹500 is now sold at ₹425. Find the percentage decrease.' Decrease = 500 - 425 = 75. % Decrease = (75/500) × 100% = 15%.

Finding New Value After Change

After increase: New value = Original × (100 + P%) / 100. After decrease: New value = Original × (100 - P%) / 100.

Example: 'Increase ₹250 by 12%.' New value = 250 × (112/100) = 250 × 1.12 = ₹280.

6. Applications of Percentage

In Tests

'Marks obtained: 46 out of 80. What percentage?' Percentage = (46/80) × 100 = 57.5%.

In Votes

'In an election, candidate A got 45% of 20,000 votes. How many votes did A get?' 45% of 20,000 = (45/100) × 20,000 = 9,000 votes.

In Data Interpretation

Reading percentage values from pie charts and bar graphs.

7. ICSE Exam Focus

Common Mistakes

1. Forgetting to multiply by 100 when converting fraction to percentage.
2. Wrong base — percentage increase/decrease is calculated on ORIGINAL value, NOT the new value.
3. Adding percentages directly when bases are different (e.g., 10% of ₹100 + 10% of ₹200 ≠ 20% of ₹300).

Percentage Conversion Reference Table

Self-Test (5 Questions)

Q1. Convert 5/8 to percentage. (1 mark)

• A) 50%
• B) 60%
• C) 62.5%
• D) 65%

Q2. Find: 12.5% of 160. (2 marks)

Q3. What percent is 45 minutes of 2 hours? (2 marks)

Q4. 'The price of a book increased from ₹240 to ₹300. Find the percentage increase.' (2 marks)

Q5. 'After a 15% discount, a watch costs ₹1,700. What was the original price?' (3 marks)

• A) ₹2,000
• B) ₹1,955
• C) ₹2,100
• D) ₹1,850

Answers

A1. C) 62.5%. (5/8 × 100 = 62.5%.) A2. 20. (12.5/100 × 160 = 1/8 × 160 = 20.) A3. 37.5%. (2 hours = 120 min. 45/120 × 100 = 37.5%.) A4. 25%. (Increase = 60. 60/240 × 100 = 25%.) A5. A) ₹2,000. (After 15% discount, SP = 85% of MP. MP = 1700 × 100/85 = ₹2,000.)