Percentages are one of the most scoring and predictable topics in Quantitative Aptitude. Students often struggle not because the formulas are difficult, but because percentage-based questions change their form depending on increase, decrease, population growth, or depreciation. Understanding how percentages relate to fractions, ratios, and basic arithmetic helps you solve any question smoothly.

If you understand these three ideas:
✔ The meaning of percentage
✔ How to convert between percent, fraction, and decimal
✔ How percentage increase/decrease works

Then you can solve ANY percentage question effortlessly.

This Percentage Formulas and Concepts covers all rules, shortcuts, applications, solved patterns, and FAQs, making it a complete one-stop resource for SSC, Banking, RRB, UPSC CSAT, and campus exams.

Quick Overview: Percentage Formulas

Concept / Situation	Meaning / Use	Formula
Convert % → Fraction	x% = x per 100	x/100
Convert fraction → %	Multiply by 100	a/b×100%
Percentage Increase	Increase in value	New Value = Old Value × 1+(R/100)
Percentage Decrease	Decrease in value	New Value = Old Value × 1−(R/100)
Change in consumption when price ↑	Reduce consumption	R/(100+R)×100%
Change in consumption when price ↓	Increase consumption	R/(100−R)×100%
Population growth	Population after n years	P(1+R/100)n
Population n years ago	Reverse population	P/(1+R/100)n
Depreciation	Value after n years	P(1−R/100)n
Depreciation reverse	Value n years ago	P/(1−R/100)n
“A is R% more than B”	Reverse %	B is less by R/(100+R)×100%
“A is R% less than B”	Reverse %	B is more by R/(100−R)×100%

Formulas for Percentage

Percentage formulas form the base of many aptitude topics such as Profit–Loss, Simple & Compound Interest, Population Growth, Depreciation, Ratio–Proportion, Data Interpretation, and more. Since exams frequently mix percentage with fractions, ratios, and repeated changes, using the correct formula becomes extremely important.
Before solving percentage questions, always convert values into proper form (fraction/decimal/percent) and identify the correct base value.

Percentage Conversion Formulas

Percentage conversion is the first step in solving any percentage-based problem. Many students directly calculate using % values, which leads to mistakes. Always convert into fraction or decimal form when needed.

1. Convert Percent to Fraction

Percent literally means per hundred.
So converting % to fraction becomes simple:

x%= x/100

This helps simplify calculations in profit, loss, interest, and ratio problems.

Example:

20% = 20/100 = 1/5

Common exam conversions:

• 25% = 1/4
• 50% = 1/2
• 12.5% = 1/8
• 10% = 1/10

2. Convert Fraction to Percent

When a value is given in fraction and needs to be expressed in percent:

a/b×100%

Example:

1/4×100 = 25%

Fraction → Percent is heavily used in DI and ratio-based questions.

Basic Percentage Change Formulas (Foundation of Percentage Problems)

All percentage questions are built on these change formulas. They define how values grow or shrink. Every exam question involving increase, decrease, consumption, discount, salary, population, or depreciation uses these three base ideas.

Percentage Increase

When a value rises by R%, the new value becomes:

New Value = Old Value(1+R/100)

Example:

If salary increases by 10% from 20,000

20,000 × 1.10 = 22,000 

Percentage Decrease

When a value decreases by R%, the new value becomes:

New Value = Old Value(1 − R/100)

Example:

Price drops 20% from 500

500 × 0.80 = 400 

Consumption vs Price Change Formulas

Just like trains have different formulas depending on direction and object length, percentage questions have separate formulas depending on whether you want to maintain expenditure or calculate change in consumption.

1. Price Increases - Consumption Must Decrease

If price increases by R%, consumption must decrease by:

R/(100+R)×100%

This keeps total expenditure constant.

Why this formula works?

Because as price goes up, you must buy less to keep spending the same.

Example:

Price ↑ 25%
Consumption ↓

(25/125)×100 = 20%

2. Price Decreases - Consumption Must Increase

If price decreases by R%, consumption increases by:

R/(100−R)×100%

Example:

Price ↓ 20%
Consumption ↑

20/80×100 = 25%

Population Change Formulas (Percentage Growth Over Years)

Just as “relative speed” is required when trains move, “compound percentage” is required when population changes every year.

Population always grows on the new population, NOT the original one.
Hence compounding is used.

1. Population After n Years

P(1+R/100)n

Where:
P = current population
R = annual growth percentage
n = number of years

Example:

Population = 50,000
Growth = 5%
2 years later:

50,000(1.05)2 = 55,125

2. Population n Years Ago

Reverse formula:

P(1+R/100)n

Depreciation Formulas

Depreciation is the opposite of population growth. Machines, vehicles, and electronics usually lose value every year at a given percentage.

1. Value After n Years

P(1−R/100)n

Example:

Value = 1,00,000
Depreciation = 10%

1,00,000×(0.9)1 = 90,000 

2. Value n Years Ago

Reverse depreciation:

P(1−R/100)n​ 

Comparison Formulas

This is similar to the “speed ratio after meeting” formula in trains, used heavily in reasoning and percentage comparison.

1. If A is R% More Than B

Then B is less than A by:

(R/100+R)×100%

Example:

A = 20% more than B
B is less by:

(20/120)×100 = 16.66% 

2. If A is R% Less Than B

Then B is more than A by:

(R/100−R)×100%

Example:

A is 20% less than B
Then B is 25% more than A.

Smart Tips and Practical Tricks for Solving Percentage Problems

Mastering Percentage becomes simple when you understand how base values, fractional conversions, and percentage changes relate to each other. Most students make mistakes not because formulas are difficult, but because they apply them without checking the reference base or the direction of change. This section breaks down the most important concepts into clear, actionable tips so you can solve questions faster and without confusion.

1. Convert Percentages into Fractions First

Students often jump directly into calculations using % values. But converting into fractions simplifies everything, especially increase, decrease, population, or depreciation problems.

Common conversions:

• 20% = 1/5
• 25% = 1/4
• 50% = 1/2
• 12.5% = 1/8
• 10% = 1/10

Example:

Find 20% of 450

1/5×450 = 90

This one step reduces long calculations and helps you solve mentally.

2. Identify the Correct Base Value Before Applying Percentage

This is the most common mistake in percentage questions.
The base value changes depending on the situation:

• Increase % → base = original value
• Decrease % → base = original value
• A is R% more than B → base = B
• A is R% less than B → base = B
• Reverse percentage → base changes completely

Example:

A is 20% more than B.
Then A = 1.2B

But reverse?
B is not 20% less than A.
You must change the base.

3. Use Percentage Change Shortcuts Instead of Long Multiplication

Percentage increase:

New = Old×(1+R/100)

Percentage decrease:

New=Old×(1−R/100)

These are faster and prevent mistakes in exam pressure.

Example:

Price rises by 25%

New Price = P×1.25

4. Always Check Whether the Percentage Change is Single or Repeated

Single change → apply only once
Repeated yearly change → use compounding

Example:

Population = 50,000
Growth = 4%
2 years later =

50,000×(1.04)2

This avoids mixing simple and compound change.

5. Use Reverse Percentage for Discount-Type or “Original Price” Questions

When the final value is given after a percentage change, reverse the formula.

Reverse % formula:
If A is R% more than B →
B is less than A by

R/(R+100)×100%

If A is R% less than B →
B is more than A by

R/(100−R)×100%

Example:

A is 25% more than B
Then B is 20% less than A, not 25%.

6. Use Complement Values for Quick Mental Calculation

Some values are easier when converted to complements:

• 100% – 20% = 80%
• 100% – 35% = 65%
• 100% + 30% = 130%

Example:

70% of 250

0.7×250 = 175 

7. Practice Typical Exam Patterns

Percentage questions combine with:

• Profit & Loss
• Simple Interest
• Compound Interest
• Ratio & Proportion
• Population
• Depreciation
• Data Interpretation
• Mixtures

Practicing these integrated patterns helps solve multi-step questions quickly in competitive exams such as SSC, Banking, Railways, UPSC CSAT, and campus placements.

FAQs About Percentage

Q1. Why do we convert percentages into fractions first?

Because fractions reduce calculation length and prevent errors.

Example:

Find 12.5% of 320

12.5% = 1/8​ 
320÷8 = 40 

Q2. Why does the base value matter in percentage problems?

Because the same percentage gives different results when the base changes.

Example:

20% of 100 = 20
20% of 200 = 40

Same percent, different base → different answer.

Q3. Why are increase/decrease formulas used instead of direct calculation?

They eliminate unnecessary multiplication and provide direct results.

Example:

Salary = 25,000
Increase = 10%

25,000×1.10 = 27,500 

Q4. Why do we use compound percentage for population and depreciation?

Because the value changes every year, so each year’s value becomes next year’s base.

Example:

Population = 10,000
Growth = 5%
2 years later:

10,000 × (1.05)2 = 11,025 

Q5. Why does “A is R% more than B” not mean B is R% less than A?

Because the percentage increase and decrease are calculated on different bases.

Example:

A = 120
B = 100
A is 20% more than B

But B is not 20% less than A.
B is less by:

(20/120)×100 = 16.66%

Q6. How do we calculate reverse percentage quickly?

Use:

Reverse = (R/100+R)×100%

Example:

A is 25% more than B
Reverse:

(25/125) × 100 = 20%

Q7. Why is percentage decrease formula important in discount questions?

Because discount reduces value, so we apply decrease formula directly.

Example:

Selling price after 20% discount on ₹500:

500×0.80 = 400 

Q8. Why is the formula for consumption change used?

To keep total expenditure constant when price changes.

Example:

Price increases 25%
Consumption must decrease by:

25/125×100 = 20% 

Q9. How do percentage formulas help solve DI (Data Interpretation)?

Most DI graphs use % changes, so knowing quick conversions saves time and boosts accuracy.

Example:

If production increases from 400 to 500
Increase percentage =

100/400 × 100 = 25% 

Q10. Why is practice important in percentage problems?

Because percentage questions often combine multiple concepts, and regular practice helps instantly choose the correct formula.

Example:

A value first increases by 20% and then decreases by 20%
Net change =

(1.2×0.8) = 0.96

So value becomes 96% → 4% decrease.