Percentage
Percentage - Methods to calculate percentages, increase/decrease percentage, successive percentage, profit/loss percentage
Learning Content
๐ Percentage – Basics
A percentage is a mathematical method of expressing how much out of 100!
๐ What is Percent Forest?
Percentagestands for "Per Cent = Per Hundred".
๐ Meaning:25% means 25 out of 100 = 25/100 = 0.25
โญ Fundamental changes
| Change | method | example |
|---|---|---|
| Percent → Fraction | Eliminate the % and divide by 100 | 25% = 25/100 = 1/4 |
| Fraction → Percent | Multiply by 100 and add % | 3/5 = (3/5) × 100 = 60% |
| Percent → Decimal | Eliminate the % and divide by 100 | 45% = 45/100 = 0.45 |
| Decimal → Percent | Multiply by 100 and add % | 0.75 = 0.75 × 100 = 75% |
๐ Major Fraction-Percent Table
| Fraction | percent | Decimal | Fraction | percent | Decimal |
|---|---|---|---|---|---|
| 1/2 | 50% | 0.5 | 1/8 | 12.5% | 0.125 |
| 1/3 | 33โ % | 0.333 | 3/8 | 37.5% | 0.375 |
| 2/3 | 66โ % | 0.666 | 5/8 | 62.5% | 0.625 |
| 1/4 | 25% | 0.25 | 7/8 | 87.5% | 0.875 |
| 3/4 | 75% | 0.75 | 1/9 | 11.11% | 0.111 |
| 1/5 | 20% | 0.2 | 1/10 | 10% | 0.1 |
| 2/5 | 40% | 0.4 | 1/11 | 9.09% | 0.0909 |
| 3/5 | 60% | 0.6 | 1/12 | 8.33% | 0.0833 |
| 4/5 | 80% | 0.8 | 1/15 | 6.67% | 0.0667 |
| 1/6 | 16โ % | 0.166 | 1/20 | 5% | 0.05 |
| 5/6 | 83โ % | 0.833 | 1/25 | 4% | 0.04 |
๐ข Basic percentage calculations
| Question type | formula | example |
|---|---|---|
| What is Y% of X? | (X × Y) / 100 | 15% of 200 = (200 × 15)/100 = 30 |
| What % of Y is X? | (X / Y) × 100 | What % of 200 is 30? = (30/200) × 100 = 15% |
| If Y% is X, total? | (X × 100) / Y | If 15% = 30, Total = (30 × 100)/15 = 200 |
๐๐ Increment & Decrement
๐ Percentage increase
New Value = Old Value × (1 + r/100)
Increase % = [(New – Old) / Old] × 100
๐ Percentage reduction
New Value = Old Value × (1 - r/100)
Reduction % = [(Old – New) / Old] × 100
๐ Percent - Key Formulas
Most Important Percentage Formulas for TNPSC Exam!
๐ข Basic formulas
| Type | formula |
|---|---|
| Y% of X | = (X × Y) / 100 |
| What % of X is Y? | = (X / Y) × 100 |
| If Y% = X, Total | = (X × 100) / Y |
| a% of b | = b% of a(Commutative Property) |
๐ Increment formulas
| Type | formula |
|---|---|
| New value after r% increment | = old value × (100 + r) / 100 |
| Percentage of increase | = [(New – Old) / Old] × 100 |
| Increase amount | = old value × r / 100 |
| Value before escalation | = new value × 100 / (100 + r) |
๐ Reduction Formulas
| Type | formula |
|---|---|
| r% is the new value after reduction | = old value × (100 - r) / 100 |
| Reduction percentage | = [(Old – New) / Old] × 100 |
| Reduction amount | = old value × r / 100 |
| Value before reduction | = new value × 100 / (100 - r) |
๐ Successive Percentage Change
| Type | formula |
|---|---|
| Two increments (a%, b%) | Net increase = a + b + (ab/100) % |
| Two reductions (a%, b%) | Net reduction = -a - b + (ab/100) % |
| Increase a%, decrease b% | Net change = a - b - (ab/100) % |
| equal increase decrease (a%, a%) | Net reduction = -(a²/100) %(Always discount!) |
๐ฅ Population formulas
| Type | formula |
|---|---|
| Population (increase) after n years | P × (1 + r/100)โฟ |
| Population (decrease) after n years | P × (1 − r/100)โฟ |
| Population n years ago | P / (1 + r/100)โฟ |
๐ฐ Price conversion formulas
| Type | formula |
|---|---|
| Increase in price r%, decrease in consumption % | = [r / (100 + r)] × 100 % |
| Reduction in price r%, increase in consumption % | = [r / (100 - r)] × 100 % |
| To keep costs constant | Increase in price % = Decrease in consumption % |
๐ Selection formulas
| Type | formula |
|---|---|
| Pass percentage | = (Qualified / Total) × 100 |
| Failure percentage | = 100 – Pass percentage |
| Marks required for passing | = Total Marks × Pass % / 100 |
๐ Percent - 10 key examples
TNPSC Model Questions with Step by Step Solutions!
๐ Example 1: Basic Percent
Question:What is 24% of 450?
Formula: Y% of X = (X × Y) / 100
= (450 × 24) / 100
= 10800 / 100
=108
๐ Example 2: Finding percentages
Question:75 is what percent of 300?
Formula: (X / Y) × 100
= (75 / 300) × 100
= 0.25 × 100
=25%
๐ Example 3: Total detection
Question:If 15% of a number = 45, what is that number?
Formula: Total = (X × 100) / Y
= (45 × 100) / 15
= 4500 / 15
=300
๐ Example 4: Percentage of increase
Question:The price of an item increased from โน800 to โน920. What is the percentage of increase?
Increase = 920 - 800 = 120
Increase % = (Increase / Old Price) × 100
= (120 / 800) × 100
=15%
๐ Example 5: Reduction percentage
Question:A city's population decreases from 50000 to 45000. What is the reduction percentage?
Reduction = 50000 - 45000 = 5000
Reduction % = (Reduction / Old Value) × 100
= (5000 / 50000) × 100
=10%
๐ Example 6: Serial percentage
Question:The price of an item is first increased by 20% and then decreased by 10%. What is the net change?
Formula: a + b - (ab/100) [increase +, decrease -]
= 20 - 10 - (20 × 10)/100
= 20 - 10 - 2
=8% increase
๐ Example 7: Population Growth
Question:A city has a population of 1,00,000. If annual growth is 5%, what will be the population after 2 years?
Formula: P × (1 + r/100)โฟ
= 1,00,000 × (1 + 5/100)²
= 1,00,000 × (105/100)²
= 1,00,000 × (1.05)²
= 1,00,000 × 1.1025
=1,10,250
๐ Example 8: Price-Consumption
Question:The price of rice increased by 25%. By what % should consumption be reduced to keep costs constant?
Formula: [r / (100 + r)] × 100
= [25 / (100 + 25)] × 100
= (25 / 125) × 100
= 0.2 × 100
=20%
๐ Example 9: Exam score
Question:Raja scored 350 out of 500 marks in an exam. What is his percentage? Passed if 40% is required?
King Percentage = (350 / 500) × 100 = 70%
Required for passing = 500 × 40/100 = 200 marks
Raja got = 350 > 200
Yes, the king passed!
๐ Example 10: TNPSC Model
Question:A number is first increased by 20% and then decreased by 20%. What is the final change?
Equivalent increase-decrease formula: -(a²/100)%
= -(20²/100)%
= -(400/100)%
=-4% (reduction)
20% increase: 100 + 20 = 120
20% reduction: 120 - 24 = 96
Net change: 100 - 96 = 4 Reduction = 4%
๐ก Important Notes:
- Increase/decrease alwaysof old valueCalculated based on
- Order is not important in serial percentages (Commutative).
- Equal increase-decrease is always netreductionwill give
- Memorize the fraction-percentage table
โก Percent Forest - Shortcuts & Tricks
Use These Shortcuts to Save Time in TNPSC Exam!
๐ Shortcut 1: Quick percentage calculation
| percent | Quick method | example |
|---|---|---|
| 1% | Divide by 100 | 1% of 450 = 4.5 |
| 10% | Divide by 10 (move the decimal point) | 10% of 450 = 45 |
| 5% | Find 10% and divide by 2 | 5% of 450 = 22.5 |
| 15% | 10% + 5% | 15% of 450 = 45 + 22.5 = 67.5 |
| 20% | Divide by 5 | 20% of 450 = 90 |
| 25% | Divide by 4 | 25% of 400 = 100 |
| 50% | Divide by 2 | 50% of 450 = 225 |
| 75% | Divide by 4 and multiply by 3 | 75% of 400 = 300 |
| 33โ % | Divide by 3 | 33โ % of 450 = 150 |
| 66โ % | Divide by 3 and multiply by 2 | 66โ % of 450 = 300 |
๐ Shortcut 2: a% of b = b% of a
| Rule: | a% of b = b% of a (Commutative Property) |
| Example: | 24% of 50 = ? Change this to 50% of 24 = 24 / 2 =12 16% of 25 = 25% of 16 = 16/4 =4 |
๐ Shortcut 3: Continuous percentage shortcut method
| Type | formula | example |
|---|---|---|
| An increase of two | a + b + ab/100 | 10% + 20% = 10 + 20 + 2 = 32% |
| Reduction of two | -(a + b - ab/100) | -10% - 20% = -(30 - 2) = -28% |
| Increase & Decrease | a - b - ab/100 | 20% up, 10% down = 20 - 10 - 2 = 8% |
| equal to a%, a% | -a²/100 | 10% up, 10% down = -1% |
๐ Shortcut 4: Fractional-percentage conversion
| Fraction | percent | Fraction | percent |
|---|---|---|---|
| 1/2 | 50% | 1/7 | 14.28% |
| 1/3 | 33.33% | 1/8 | 12.5% |
| 1/4 | 25% | 1/9 | 11.11% |
| 1/5 | 20% | 1/10 | 10% |
| 1/6 | 16.67% | 1/11 | 9.09% |
๐ Shortcut 5: Price-Consumption Quick Table
| Price change | Change in Consumption (No Change in Expenditure) |
|---|---|
| 10% increase | 9.09% reduction (1/11) |
| 20% increase | 16.67% reduction (1/6) |
| 25% increase | 20% off (1/5) |
| A 33โ % increase | 25% off (1/4) |
| 50% increase | 33โ % reduction (1/3) |
| 100% increase | 50% off (1/2) |
๐ Shortcut 6: Percentage conversion shortcut
| Increase %: | 500 → 600 but? Change = 100, Base = 500 % = (100/500) × 100 =20% |
| Shortcut: | 600/500 = 6/5 = 1.2 = 120% Increase = 120% - 100% =20% |
๐ Shortcut 7: Population Quick Calculation
| 10% growth, 2 years: | P × 1.1² = P × 1.21 Simple formula: P + P×21% = P × 1.21 |
| 10% growth, 3 years: | P × 1.1³ = P × 1.331 Simple formula: P + P×33.1% |
1.1² = 1.21 (21% increase)
1.1³ = 1.331 (33.1% increase)
1.2² = 1.44 (44% increase)
๐ Shortcut 8: Exam Score Quick Method
| Question: | 350/500 = how many %? |
| Quick Method: | 350/500 = 35/50 = 7/10 =70% (or) 350 × 2 / 10 = 700/10 = 70% |
๐ Shortcut 9: Percentage comparison
| Question: | How much is 60 out of 300 out of 500? |
| Solution: | 60/300 = x/500 x = (60 × 500) / 300 = 30000/300 =100 |
| Shortcut: | 60 is 20% of 300 20% of 500 =100 |
๐ Shortcut 10: Simple Fraction Percent
| question | Shortcut | answer |
|---|---|---|
| 37.5% of 80 | 3/8 × 80 | 30 |
| 62.5% of 64 | 5/8 × 64 | 40 |
| 87.5% of 56 | 7/8 × 56 | 49 |
| 12.5% โโof 96 | 1/8 × 96 | 12 |
| 16.67% of 72 | 1/6 × 72 | 12 |
| 83.33% of 60 | 5/6 × 60 | 50 |
๐ฏ TNPSC Exam Tips:
- Memorize the fraction-percentage table
- Apply the rule a% of b = b% of a
- Find 10%, 5%, 1% and calculate the rest
- Don't forget to add/subtract ab/100 to the serial percentage
- Do backward calculation from Options
โฑ๏ธ Time Management:
- Only 30-45 seconds per question
- Skip difficult questions and try later
- Do mental math practice without calculator
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