Percentage - All Formulas & Shortcuts

Quick reference guide for all Percentage formulas with lightning-fast calculation tricks

📘 Basic Formulas

1. Percentage Definition

Percentage = (Part / Whole) × 100

Finding Part:

Part = (Percentage × Whole) / 100

Finding Whole:

Whole = (Part × 100) / Percentage

2. Fraction to Percentage

Percentage = Fraction × 100

Example:

3/4 = (3/4) × 100 = 75%

3. Percentage to Fraction

Fraction = Percentage / 100

Example:

25% = 25/100 = 1/4

🎯 Important Conversions (MEMORIZE!)

Fraction ↔ Percentage Conversion Table

• 1/3 = 33.33%, 2/3 = 66.67% (doubles)
• 1/6 = 16.67%, 5/6 = 83.33% (half of 1/3)
• 1/8 = 12.5% (half of 25%)
• 1/5 = 20% (easy: 100/5)

⚡ Quick Calculation Shortcuts

4. Finding Percentage of a Number

Method 1: Traditional

20% of 350 = (20/100) × 350 = 70

Method 2: Quick Trick

20% = 1/5 20% of 350 = 350/5 = 70

Shortcut Table:

%	Quick Method
10%	Divide by 10
20%	Divide by 5
25%	Divide by 4
50%	Divide by 2
5%	Divide by 20 OR (10% ÷ 2)
15%	(10% + 5%)
30%	(10% × 3)
75%	(100% - 25%)

5. Percentage Increase/Decrease

Increase:

New Value = Original × (1 + Increase%/100)

Decrease:

New Value = Original × (1 - Decrease%/100)

Finding Percentage Change:

% Change = [(New - Old) / Old] × 100

Increase: Positive result Decrease: Negative result

6. Successive Percentage Changes

Two successive changes R₁% and R₂%:

Net Change = R₁ + R₂ + (R₁ × R₂)/100

Example: 20% increase then 10% decrease

Net = 20 + (-10) + [20 × (-10)]/100 = 20 - 10 - 2 = 8% increase

Three successive changes:

Final = Original × (1 ± R₁/100)(1 ± R₂/100)(1 ± R₃/100)

7. Quick Successive Change Patterns

Two equal increases of R%:

Net = 2R + R²/100

Two equal decreases of R%:

Net = -2R + R²/100

One increase R%, one decrease R%:

Net = -(R²/100) [Always a loss!]

Example: 10% increase, 10% decrease

Net = -(10²/100) = -1% (loss)

💡 Percentage Increase/Decrease Shortcuts

8. Common Increase Percentages

Original	New	% Increase	Quick Formula
100	110	10%	+10%
100	120	20%	+20%
100	125	25%	+25%
100	150	50%	+50%
100	200	100%	Doubles
100	300	200%	Triples

9. Common Decrease Percentages

Original	New	% Decrease	Quick Formula
100	90	10%	-10%
100	80	20%	-20%
100	75	25%	-25%
100	50	50%	Halves
100	25	75%	Quarter left

10. Reverse Percentage (Finding Original Value)

If new value after R% increase is N:

Original = N / (1 + R/100) OR Original = N × 100 / (100 + R)

If new value after R% decrease is N:

Original = N / (1 - R/100) OR Original = N × 100 / (100 - R)

Quick Examples:

• After 25% increase, value = 500 → Original = 500 × 100/125 = 400
• After 20% decrease, value = 400 → Original = 400 × 100/80 = 500

🎓 Advanced Percentage Tricks

11. Percentage Point Difference

Important: “Percentage points” ≠ “Percentage”

Example:

• Score increased from 40% to 60%
• Percentage point increase: 60 - 40 = 20 percentage points
• Percentage increase: (20/40) × 100 = 50%

12. Two Numbers Comparison

If A is R% more than B:

A = B(1 + R/100) B = A(100/(100 + R))

B is what % less than A:

% less = R/(100 + R) × 100

Example: A is 25% more than B

• B is what % less than A?
• % = 25/125 × 100 = 20%

Quick Pattern Table:

A is…more	B is…less
10% more	9.09% less
20% more	16.67% less
25% more	20% less
50% more	33.33% less
100% more (double)	50% less (half)

13. Ratio to Percentage

If ratio A:B = m:n

A’s share %:

A% = [m/(m+n)] × 100

B’s share %:

B% = [n/(m+n)] × 100

Example: Ratio 3:2

• A% = 3/5 × 100 = 60%
• B% = 2/5 × 100 = 40%

14. Population/Value Problems

After 2 years with rates R₁% and R₂%:

Final = Initial × (1 + R₁/100)(1 + R₂/100)

For same rate R% for T years:

Final = Initial × (1 + R/100)^T

🔥 Mental Math Techniques

15. Quick Percentage of Numbers

For multiples of 100:

15% of 200 = 15 × 2 = 30

For numbers ending in 0:

12% of 350 = 12 × 3.5 = 42

Using 10% as base:

17% of 500 = (10% + 7%) = 50 + 35 = 85

Using complements:

95% of 400 = (100% - 5%) = 400 - 20 = 380

16. Fraction Multiplication Shortcut

Instead of:

(2/3) × (3/4) × (4/5) = ?

Observe cancellation:

(2/3) × (3/4) × (4/5) = 2/5

In percentage:

66.67% × 75% × 80% = 40%

📊 Exam-Specific Patterns

Pattern 1: Income-Expenditure Problems

Given: Income I, Expenditure E Find: Savings S

Savings = Income - Expenditure Savings % = (S/I) × 100

If income increases by x% and expenditure by y%:

New Savings = I(1+x/100) - E(1+y/100)

Pattern 2: Passing Marks Problems

Given: Pass marks = P% of total Student scored: x marks (failed by y marks)

Total marks = (x + y) × 100/P

Pattern 3: Mixtures (Alligation)

Two solutions with concentrations A% and B% Final concentration: C%

Ratio of mixing:

Solution A : Solution B = (C - B) : (A - C)

Pattern 4: Profit/Loss Percentage

Cost Price (CP), Selling Price (SP)

Profit/Loss:

Profit = SP - CP Loss = CP - SP

Profit %:

Profit% = (Profit/CP) × 100

Loss %:

Loss% = (Loss/CP) × 100

Quick Formulas:

SP = CP(1 + Profit%/100) SP = CP(1 - Loss%/100)

🎯 Speed Calculation Tricks

Trick 1: 10% of any number

Just move decimal one place left 10% of 3,450 = 345.0

Trick 2: 5% of any number

Take 10% and halve it 5% of 880 = 88/2 = 44

Trick 3: 1% of any number

Move decimal two places left 1% of 5,600 = 56

Trick 4: 25% of any number

Divide by 4 25% of 840 = 840/4 = 210

Trick 5: 50% of any number

Divide by 2 50% of 1,234 = 617

Trick 6: 75% of any number

75% = 50% + 25% 75% of 400 = 200 + 100 = 300 OR subtract 25% from 100% 75% of 400 = 400 - 100 = 300

Trick 7: 33.33% of any number

Divide by 3 33.33% of 900 = 900/3 = 300

Trick 8: 66.67% of any number

Multiply by 2 and divide by 3 66.67% of 600 = (600 × 2)/3 = 400

💎 Golden Rules

1. Memorize fraction-percentage conversions (1/2 to 1/10)
2. Use 10% as base for other percentages
3. Successive changes: Use formula, don’t calculate separately
4. Increase then decrease by same % = Always loss of (R²/100)%
5. For reverse %: Divide by (100 ± R)
6. Quick check: Final answer should make logical sense

🔗 Related Resources

Practice Questions:

• Percentage Practice Questions

Theory:

• Percentage Theory & Concepts

Related Topics:

• Profit & Loss
• Ratio & Proportion
• Simple Interest

Study Resources:

• All-in-One Formula Sheet
• Shortcuts & Tricks Compilation

Download this formula sheet as PDF (feature coming soon)

Print and stick near your study desk! 📌

With these shortcuts, you’ll solve percentage questions in under 30 seconds! ⚡