Percentage Formula Cheat Sheet

Percentage Formula Cheat Sheet

Quick Revision

Percentage means “per hundred”.

Percentage is a fundamental quantitative aptitude topic and is used in Profit & Loss, Discount, Simple Interest, Compound Interest, Ratio, Population, Data Interpretation, and many other exam questions.

1. Basic Percentage Formulas

Example

25 is what percentage of 200?

(25 / 200) × 100 = 12.5%

2. Percentage Conversions

Fraction → Percentage

Percentage = Fraction × 100

Percentage → Fraction

Fraction = Percentage / 100

Decimal → Percentage

Percentage = Decimal × 100

Percentage → Decimal

Decimal = Percentage / 100

3. Important Fraction–Percentage Values

These conversions are useful for quick calculations.

4. Percentage Increase

When a value changes from an original value to a higher value:

Increase = New Value − Original Value

Percentage Increase
= (Increase / Original Value) × 100

Or:

Percentage Increase
= [(New Value − Original Value) / Original Value] × 100

New Value After an Increase

If the increase is r%:

New Value = Original Value × (100 + r) / 100

Example

A salary increases from ₹20,000 to ₹25,000.

Increase = 25,000 − 20,000
         = ₹5,000

Increase % = (5,000 / 20,000) × 100
           = 25%

5. Percentage Decrease

When a value changes from an original value to a lower value:

Decrease = Original Value − New Value

Percentage Decrease
= (Decrease / Original Value) × 100

Or:

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

New Value After a Decrease

If the decrease is r%:

New Value = Original Value × (100 − r) / 100

Example

A price decreases from ₹500 to ₹400.

Decrease = 500 − 400
         = ₹100

Decrease % = (100 / 500) × 100
           = 20%

6. Successive Percentage Changes

When two percentage changes are applied one after another:

Net Change = a + b + (ab / 100)

Use a negative sign for a decrease.

Example: Increase followed by Increase

A value increases by 10% and then by 20%.

Net Change
= 10 + 20 + (10 × 20)/100
= 32%

So the total increase is 32%.

Increase Followed by Decrease

For an increase of a% followed by a decrease of b%:

Net Change = a − b − (ab / 100)

Example:

Increase = 20%
Decrease = 10%

Net Change
= 20 − 10 − (20 × 10)/100
= 8%

So the final value is 8% higher than the original value.

7. Increase and Decrease by the Same Percentage

If a value is increased by x% and then decreased by x%:

Net Decrease = x² / 100 %

Example

Increase by 20%, then decrease by 20%:

Net Decrease = 20² / 100
             = 4%

The final value is therefore 4% less than the original value.

8. Reverse Percentage

If a value after an increase of r% becomes N:

Original Value = N × 100 / (100 + r)

If a value after a decrease of r% becomes N:

Original Value = N × 100 / (100 − r)

Example

After a 20% increase, a number becomes 360.

Original
= 360 × 100 / 120
= 300

9. Percentage of Percentage

To find a% of b% of a number N:

(a/100) × (b/100) × N

Example

Find 20% of 30% of 500.

20/100 × 30/100 × 500
= 30

10. Important Shortcut

a% of b = b% of a

For any two numbers a and b:

a% of b = b% of a

Example

20% of 50 = 10

50% of 20 = 10

This can make some mental calculations faster.

11. Percentage Point vs Percentage Change

Do not confuse percentage points with percentage change.

If marks increase from 40% to 50%:

Increase in percentage points
= 50 − 40
= 10 percentage points

But relative percentage increase is:

(10 / 40) × 100
= 25%

Therefore:

40% → 50%
= 10 percentage points
= 25% relative increase

12. Population Growth / Repeated Increase

For a quantity that increases by r% every year for n years:

Final Value = P × (1 + r/100)ⁿ

where:

• P = initial value
• r = percentage growth
• n = number of periods

Example

Population = 10,000 Growth = 5% per year Time = 2 years

Final Population
= 10,000 × (1 + 5/100)²
= 10,000 × 1.05²
= 11,025

For repeated decreases:

Final Value = P × (1 − r/100)ⁿ

13. Price–Consumption Shortcut

When expenditure remains constant:

If price increases by r%

Required percentage decrease in consumption:

Required Decrease
= [r / (100 + r)] × 100

If price decreases by r%

Required percentage increase in consumption:

Required Increase
= [r / (100 − r)] × 100

Example

Price increases by 25%.

Required decrease in consumption:

25 / 125 × 100
= 20%

14. Percentage and Profit & Loss

Percentage is frequently used in Profit & Loss problems.

Profit = SP − CP

Loss = CP − SP

Profit % = (Profit / CP) × 100

Loss % = (Loss / CP) × 100

Selling Price After Profit

SP = CP × (100 + Profit%) / 100

Selling Price After Loss

SP = CP × (100 − Loss%) / 100

Remember: Profit% and Loss% are normally calculated using Cost Price (CP) as the base.

15. Fast Mental Percentage Tricks

10%  = divide by 10
5%   = divide by 20
20%  = divide by 5
25%  = divide by 4
50%  = divide by 2
12.5% = divide by 8

Example

12.5% of 640:

640 ÷ 8 = 80

25% of 800:

800 ÷ 4 = 200

16. Common Mistakes

Mistake 1: Using the wrong base

Percentage increase/decrease is calculated using the original value as the base.

Increase % = Increase / Original × 100

Mistake 2: Adding successive percentages directly

A 10% increase followed by a 20% increase is not a 30% increase.

Net increase = 10 + 20 + (10 × 20)/100
             = 32%

Mistake 3: Confusing percentage points with percentage change

40% → 50% is a 10 percentage-point increase, but a 25% relative increase.

Mistake 4: Confusing Profit% with Loss%

Profit% and Loss% normally use CP, not SP, as the denominator.

17. One-Minute Revision Table

18. Exam Quick Tips

• Memorise common fraction-to-percentage conversions.
• Always identify the base/original value before calculating percentage change.
• Use fractions such as 1/2, 1/4, 1/5 and 1/8 for faster mental calculations.
• For successive changes, use the successive-percentage formula instead of adding percentages directly.
• Remember that percentage is a foundation for several arithmetic chapters, so mastering these formulas helps with related questions too.

Related Cheat Sheets: Profit & Loss Formula Cheat Sheet · Simple Interest Formula Cheat Sheet · Compound Interest Formula Cheat Sheet · Ratio & Proportion Formula Cheat Sheet