Percentage is one of the most useful arithmetic topics for SSC, Banking, Railway, and other competitive exams. It also supports later chapters such as Profit and Loss, Discount, Simple and Compound Interest, Ratio, Data Interpretation, and many word problems.
The best way to learn Percentage is not to memorise dozens of shortcuts. First understand what “per hundred” means, then become comfortable with fractions, decimals, percentage change, and reverse calculations. Once the basic logic is clear, faster methods become much easier to use safely.
What Percentage Means
Percentage simply means “out of 100.” For example, 35% means 35 out of 100, so it can also be written as 35/100 or 0.35.
The same value can often be written in three useful forms:
- 50% = 1/2 = 0.5
- 25% = 1/4 = 0.25
- 20% = 1/5 = 0.20
- 12.5% = 1/8 = 0.125
- 75% = 3/4 = 0.75
These conversions matter because the easiest form depends on the question. Sometimes a fraction is faster than multiplication, while in another question a decimal or direct percentage method is clearer.
Core Percentage Formulas
You do not need a huge formula list. A small number of reliable relationships cover most basic questions.
- x% of y = (x/100) × y
- Percentage = (Part / Whole) × 100
- Percentage change = (Change / Original value) × 100
- New value after increase = Original × (100 + increase%)/100
- New value after decrease = Original × (100 - decrease%)/100
The most important word in percentage change is original. The denominator should normally be the value from which the change started. Using the new value instead is one of the most common exam mistakes.
For a focused formula revision, use the Percentage Formulas guide.
How to Find a Percentage of a Number
Suppose you need to find 35% of 240.
Using the direct method:
35% of 240 = 35/100 × 240 = 84.
You can also split 35% into 30% + 5%. Then 30% of 240 is 72 and 5% is 12. Adding them gives 84.
Both methods are correct. During practice, learn to choose the method that reduces calculation without making the logic harder to follow.
Benchmark Percentages for Faster Calculation
Some percentages should become almost automatic because they convert cleanly into fractions.
- 10% = divide by 10
- 20% = divide by 5
- 25% = divide by 4
- 50% = divide by 2
- 75% = three-fourths
- 12.5% = one-eighth
- 33.33% is approximately one-third where the question allows that relation
- 66.67% is approximately two-thirds where appropriate
For example, 25% of 320 is easier to see as one-fourth of 320, which is 80.
For more mental methods, see Percentage Tricks for Fast Calculation.
Percentage Increase and Decrease
If a value changes from 200 to 250, the increase is 50.
Percentage increase = 50/200 × 100 = 25%.
If a price falls from 800 to 680, the decrease is 120.
Percentage decrease = 120/800 × 100 = 15%.
The base value matters. A 25% increase and a 25% decrease do not normally cancel each other because the second percentage is applied to a different value.
Successive Percentage Change
Suppose a value rises by 20% and then falls by 20%.
Start with 100. After a 20% increase it becomes 120. A 20% decrease on 120 is 24, so the final value becomes 96.
The net result is therefore a 4% decrease, not zero.
This is why successive changes should be handled with actual values or multipliers rather than by blindly adding and subtracting percentages.
Reverse Percentage
Reverse percentage questions give you the final value and ask for the original value.
For example, after a 20% increase a number becomes 360.
The final value is 120% of the original, so:
Original = 360 × 100/120 = 300.
The key is to identify what percentage of the original the final value represents.
Percentage Comparison
Statements such as “A is 25% more than B” and “B is what percent less than A?” need careful reading because the base changes.
If B = 100 and A is 25% more, then A = 125.
But B is not 25% less than A. The decrease from 125 to 100 is 25, and the base is now 125:
25/125 × 100 = 20%.
So if A is 25% more than B, B is 20% less than A.
Percentage Word Problems
Many percentage questions look difficult only because they are written as stories. Before calculating, identify:
- What is the whole?
- What is the part?
- What value is the original base?
- Is the question asking for a percentage, a value, or a change?
Translate the sentence into these relationships before choosing a formula. For a deeper treatment, use the Percentage Word Problems guide.
Fast Arithmetic Shortcuts
For awkward percentages, splitting can save time.
For example, to find 18% of 250:
- 10% = 25
- 5% = 12.5
- 2% = 5
- 1% = 2.5
Total = 25 + 12.5 + 5 + 2.5 = 45.
This method is different from memorising fraction benchmarks. It is useful when the percentage itself is awkward but can be built from easy parts.
Practise this approach in Percentage Shortcuts for Arithmetic Speed.
Common Percentage Mistakes
Percentage errors usually come from the setup, not from difficult arithmetic. Watch especially for these problems:
- Using the wrong base value.
- Treating equal percentage increase and decrease as cancellation.
- Confusing percentage points with percentage change.
- Reversing “A is x% more than B.”
- Using a memorised shortcut without understanding its condition.
- Rounding too early in the calculation.
- Reading the final value as the original value.
The detailed Common Percentage Mistakes guide shows how to recognise these traps.
Worked Examples
These examples show how the main percentage ideas work in actual calculations. Focus on the setup first, especially the base value, before trying to solve the question quickly.
Example 1: Direct Percentage
Find 12.5% of 560.
12.5% = 1/8, so 560 ÷ 8 = 70.
Example 2: Percentage Decrease
A price falls from 480 to 408. Find the percentage decrease.
Decrease = 72.
Percentage decrease = 72/480 × 100 = 15%.
Example 3: Finding the Whole
36 is what percent of 240?
36/240 × 100 = 15%.
Example 4: Reverse Percentage
After a 25% increase, a value becomes 500. Find the original value.
500 represents 125% of the original.
Original = 500 × 100/125 = 400.
How Percentage Appears in Competitive Exams
Percentage may appear as a direct question, but it is also hidden inside Profit and Loss, Discount, Interest, Ratio, Population, Marks, Data Interpretation, and comparison questions.
This is why Percentage should be understood as a foundation topic rather than a chapter to finish once and forget.
For exam-oriented formats, review Exam-Based Percentage Questions.
Previous-Year Question Patterns
When reviewing previous-exam patterns, focus on the method rather than memorising a specific number set. Similar structures often return with different values.
ExamPrepWay should clearly distinguish verified previous-year questions from practice created in the style of competitive exams. Do not assume that a practice question is an official PYQ unless its source has been verified.
Use the Previous Year Percentage Question Patterns page for this type of revision.
How to Practise Percentage Properly
A useful practice sequence is:
- Learn the basic concept and formulas.
- Practise direct percentage calculations.
- Work on increase, decrease, and reverse percentage.
- Move to comparisons and word problems.
- Add timed calculations only after accuracy is stable.
- Review every repeated mistake.
- Mix Percentage with Profit and Loss, Discount, and Data Interpretation.
Practice Set 1 already includes worked SSC CGL-style percentage questions: Percentage Practice Set 1 with Solutions.
Then continue with Percentage Practice Set 2 for another mixed set.
Last-Minute Percentage Revision
Before an exam, do not try to learn ten new tricks. Revise the conversions and methods you already trust:
- 10%, 5%, and 1% ladder
- common fraction-percentage conversions
- percentage change formula
- reverse percentage setup
- successive-change logic
- common base-value mistakes
For a compact revision page, use Percentage Speed Tricks for Last-Minute Revision.
Percentage Learning Path on ExamPrepWay
Use the cluster articles according to your current need:
- Percentage Tricks for Fast Calculation — benchmark fractions and mental methods.
- Percentage Formulas You Must Remember — formula revision.
- Common Percentage Mistakes in Exams — error prevention.
- Percentage Shortcuts for Arithmetic Speed — value splitting and quick arithmetic.
- Percentage Word Problems Explained — language-to-equation practice.
- Exam-Based Percentage Questions — competitive-exam patterns.
- Previous Year Percentage Question Patterns — recurring question structures.
- Percentage Practice Set 1 — solved practice.
- Percentage Practice Set 2 — additional mixed practice.
- Percentage Speed Tricks for Last-Minute Revision — quick revision.
What to Do Next
If your accuracy is still weak, return to direct calculations and percentage change before chasing speed. If your basics are strong, move into word problems, Profit and Loss, Discount, and mixed arithmetic practice.
The goal is simple: understand the base, choose a reliable method, calculate carefully, and learn from repeated mistakes. Once that process becomes automatic, Percentage becomes one of the most useful tools in arithmetic.