Percentage is one of the most important concepts in SSC CGL Mathematics. It appears directly in percentage questions and indirectly in Profit & Loss, Discount, Simple & Compound Interest, Population, Data Interpretation, and Ratio. Instead of memorising dozens of formulas, this guide helps you learn the core ideas and understand how they connect — with interactive mini quizzes after every major concept so you can test yourself before the real exam.
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1. What is Percentage?
The word percentage means "per hundred." The symbol used for percentage is %.
x% = x / 100
For example:
- 50% = 50/100 = 1/2
- 25% = 25/100 = 1/4
- 75% = 75/100 = 3/4
Percentage simply represents a quantity out of 100.
Percentage, Fraction & Decimal
The same value can be represented in three forms. For example:
- 50% = 1/2 = 0.5
- 25% = 1/4 = 0.25
- 75% = 3/4 = 0.75
This conversion is extremely useful in SSC because fractions are often faster to calculate with than percentages.
2. Percentage Conversions
Fraction → Percentage
Multiply the fraction by 100.
Percentage = Fraction × 100
Example: Convert 3/4 into percentage → 3/4 × 100 = 75%. Another example: 5/8 × 100 = 62.5%.
Percentage → Fraction
Write the percentage over 100 and simplify.
x% = x / 100
Example: 40% = 40/100 = 2/5. And 12.5% = 12.5/100 = 1/8.
Decimal → Percentage
Multiply by 100. Examples: 0.5 = 50%, 0.75 = 75%, 1.25 = 125%.
SSC Tip
You don't need to memorise every value in the table. Prioritise 50%, 25%, 20%, 10%, 12.5%, 33⅓%, 66⅔%, 37.5% and 75% — these frequently make mental calculations much faster.
What is 37.5% as a fraction?
What percentage is 5/8?
3. Basic Percentage Calculations
There are three basic types of percentage questions.
Type 1: Find x% of a number
x% of y = (x × y) / 100
Example: Find 20% of 500 → (20 × 500)/100 = 100.
⚡ Faster method: 20% = 1/5, so 500 ÷ 5 = 100. No multiplication required.
Type 2: Find what percentage one number is of another
Percentage = (Part / Whole) × 100
Example: 25 is what percentage of 200? → (25/200) × 100 = 12.5%.
Type 3: Find the original number
Original Number = (x × 100) / y
Example: 60 is 15% of a number → (60 × 100)/15 = 400. Verification: 400 × 15% = 60. Correct.
What is 15% of 650?
45 is 18% of which number?
4. Percentage Increase & Decrease
This is one of the most important applications of percentage.
Percentage Increase
% Increase = ((New − Original) / Original) × 100
Example: Salary increases from ₹20,000 to ₹25,000. Increase = ₹5,000. Percentage increase = (5000/20000) × 100 = 25%.
Percentage Decrease
% Decrease = ((Original − New) / Original) × 100
Example: Price decreases from ₹500 to ₹400. Decrease = ₹100. Percentage decrease = (100/500) × 100 = 20%.
The Most Important Rule
Percentage change is always calculated using the original value as the base — never the new value. For ₹100 → ₹120, the increase is ₹20, so the percentage increase is (20/100) × 100 = 20%, not (20/120) × 100.
Finding the New Value After a Percentage Change
After x% increase: New Value = Original × (100 + x)/100
After x% decrease: New Value = Original × (100 − x)/100
Example: 800 increases by 25% → 800 × 125/100 = 1000. Example: 1200 decreases by 20% → 1200 × 80/100 = 960.
A salary increases from ₹20,000 to ₹25,000. What is the percentage increase?
A number is increased by 25%. If the original number is 800, what is the new value?
5. Successive Percentage Changes
Suppose a value changes by two percentages one after another. You cannot simply add the percentages because the second percentage is calculated on the already changed value. For two successive changes x% and y% (treat increases as positive and decreases as negative):
Net Change = x + y + (xy / 100)
Example 1: Two Increases
Price increases by 10% and then 20% → 10 + 20 + (10×20)/100 = 32% net increase.
Example 2: Increase Followed by Decrease
Population increases by 20% and then decreases by 10% → 20 − 10 + (20×−10)/100 = 8% net increase.
Example 3: Decrease Followed by Increase
Price decreases by 25% and then increases by 25% → −25 + 25 + (−25×25)/100 = 6.25% net decrease.
Equal Increase and Decrease
If a value increases by x% and then decreases by the same x%, the net effect is always a decrease of x²/100 percent. For 20%: 20²/100 = 4% decrease. It never returns to the original value.
A number increases by 10% and then by 20%. What is the net increase?
A number increases by 20% and then decreases by 20%. What is the net change?
A price decreases by 25% and then increases by 25%. What is the final change?
6. Reverse Percentage
Sometimes a value changes by a percentage and the question asks: what percentage change is required to return to the original value? The answer is not the same percentage.
If a Value Increases by x%
Required decrease = (x / (100 + x)) × 100
Example: Price increases by 25% → required decrease = (25/125) × 100 = 20%. Verification: 100 → 125 (after +25%) → 125 − 20% of 125 = 125 − 25 = 100. Correct.
If a Value Decreases by x%
Required increase = (x / (100 − x)) × 100
Example: Salary decreases by 20% → required increase = (20/80) × 100 = 25%.
🧠Remember: for an increase, the required decrease uses the larger denominator (100 + x); for a decrease, the required increase uses the smaller denominator (100 − x).
A price increases by 40%. What percentage decrease is required to bring it back to its original value?
A salary decreases by 20%. What percentage increase is required to restore the original salary?
7. Percentage + Population
Population questions are essentially successive percentage-change questions. If population increases by the same rate r% every year:
P(final) = P × (1 + r/100)â¿
where n = number of years. For a decrease of r% per year:
P(final) = P × (1 − r/100)â¿
Example: Population 10,000 grows at 5% for 2 years → 10000 × (1.05)² = 11,025.
The population of a town is 8,000. It increases by 10% per year. What will it be after 2 years?
A population of 10,000 decreases by 10% every year. What will it be after 2 years?
8. Percentage + Profit & Loss
Percentage is also the foundation of Profit & Loss. CP = Cost Price, SP = Selling Price.
Profit% = (Profit / CP) × 100
Loss% = (Loss / CP) × 100
Example: CP = ₹800, SP = ₹960. Profit = ₹160. Profit% = (160/800) × 100 = 20%.
SP after p% profit = CP × (100 + p)/100
SP after p% loss = CP × (100 − p)/100
Example: CP = ₹2,000, Loss = 15% → SP = 2000 × 85/100 = ₹1,700.
SSC Trap
Profit percentage is always calculated on CP, never on SP. If CP = ₹100 and SP = ₹120, profit = ₹20, so profit% = 20% (using CP as base).
An article bought for ₹1,200 is sold for ₹1,500. Find the profit percentage.
An article is sold at a 15% loss. If CP = ₹2,000, find SP.
9. Percentage Point vs Percentage Increase
This is a subtle but important distinction. Suppose marks increase from 40% to 50%. The percentage-point increase is 50 − 40 = 10 points. But the relative percentage increase is (10/40) × 100 = 25%.
So: 40% → 50% is a 10 percentage-point increase, but a 25% relative increase. Don't confuse the two.
A student's score increases from 60% to 75%. What is the relative percentage increase?
âš¡ SSC Percentage Shortcuts
10% and 5%
For 10%, simply divide by 10. For 5%, find 10% and halve it. 10% of 450 = 45; 5% of 600 = 60 ÷ 2 = 30.
50%, 25% and 20%
50% = divide by 2, 25% = divide by 4, 20% = divide by 5. 50% of 840 = 420; 25% of 800 = 200; 20% of 750 = 150.
12.5% and 75%
12.5% = divide by 8: 640/8 = 80. 75% = find 3/4: 800 × 3/4 = 600.
Swap Percentage
x% of y = y% of x. So 16% of 25 becomes 25% of 16 = 4 — very useful for mental calculations.
âš ï¸ Common SSC Percentage Mistakes
- Adding successive percentages directly: 10% + 20% is not 30%. The correct answer is 32% increase.
- Assuming equal increase and decrease cancel out: A 20% increase followed by a 20% decrease is not 0% — it is a 4% decrease.
- Using the wrong base: Percentage increase/decrease always uses the original value as the base, not the new value.
- Using SP instead of CP for Profit%: Profit percentage is always calculated on the Cost Price.
- Treating reverse percentage as the same percentage: A 25% increase requires a 20% decrease to reverse, not 25%.
- Confusing percentage points with percentage increase: 40% → 50% is 10 percentage points, but a 25% relative increase.
🧠Percentage Formula Sheet
🆠Final Percentage Revision Quiz
You've now covered the complete module. Don't look back at the formulas — try these mixed questions first.
What is 12.5% of 640?
45 is what percentage of 180?
A number increases by 20% and then decreases by 20%. What is the net change?
A price increases by 40%. What percentage decrease will restore the original price?
A population of 8,000 grows by 10% annually. What will it be after 2 years?
An article costing ₹1,200 is sold for ₹1,500. Find the profit percentage.
A number increases by 30% and then decreases by 10%. Find the net change.
A salary decreases by 20%. What percentage increase is needed to restore the original salary?
Marks increase from 40% to 50%. What is the relative percentage increase?
If 40% of A = 60% of B, then A : B is:
How to Prepare Percentage for SSC CGL
Don't try to memorise this entire article. Use this progression instead:
1. Learn
Understand the flow: Percentage → Change → Successive Change → Reverse Percentage. Concepts build on each other.
2. Memorise
Learn the common fraction-percentage conversions and the basic shortcuts by heart.
3. Practice
Solve questions covering different patterns rather than solving 20 identical questions in a row.
4. Analyse & Attempt PYQs
When you get a question wrong, identify the exact concept that caused it. Once concepts are clear, move to actual SSC previous-year questions.
Why This Topic Matters
Percentage underlies Profit & Loss, Simple & Compound Interest, Population, Data Interpretation, and Ratio questions across SSC CGL Tier 1 and Tier 2. Mastering this one concept meaningfully boosts your Quantitative Aptitude score across multiple topics at once.