Core ConceptRead this first — the foundation of the topic
Basic Percentage is the foundation of all percentage problems in SSC CGL. It measures parts per hundred. The word 'percent' comes from Latin 'per centum' meaning 'by hundred'. Understanding this concept is crucial as it appears in 2-3 questions in every SSC CGL paper. Core Concept: Percentage is a way to express a fraction with denominator 100. When you say 25%, it means 25 out of 100 parts. Think of it as cutting a pie into 100 equal slices and taking some of them.
Key RulesCore rules you must know cold
First, percentage is always calculated on a base value. Second, 100% means the complete quantity. Third, percentages can exceed 100% when the part is larger than the whole. Fourth, percentage change and percentage of a number are different concepts.
Formula BlockMemorise — at least one formula appears in every paper
• Percentage = (Part/Whole) × 100
• Part = (Percentage/100) × Whole
• Whole = (Part × 100)/Percentage
• Percentage to Fraction: x% = x/100
• Percentage to Decimal: x% = x/100 = 0.0x
Exam PatternsWhat examiners ask — read before attempting PYQs
Powerful Shortcuts for Quick Calculation
Shortcut 1 - Common Percentage Conversions:
• 50% = 1/2, 25% = 1/4, 20% = 1/5, 10% = 1/10
• 33.33% = 1/3, 66.67% = 2/3, 12.5% = 1/8, 16.67% = 1/6
Memorize these to solve faster without calculations
Shortcut 2 - Quick Mental Math Trick
• For 15% of any number: Take 10% + 5%
• For 35% of any number: Take 30% + 5%
• Break complex percentages into easier chunks
Worked ExampleSolve this step-by-step before moving on
1
Step 1
Convert percentage to decimal: 24% = 24/100 = 0.24
Add: 170 + 34 = 204
Answer: 24% of 850 = 204
Worked Example 2: What percentage is 156 of 240?
1
Step 1
Use formula: Percentage = (Part/Whole) × 100
2
Step 2
Substitute values: (156/240) × 100
3
Step 3
Simplify fraction: 156/240 = 13/20 (dividing by 12)
4
Step 4
Convert to decimal: 13/20 = 0.65
5
Step 5
Multiply by 100: 0.65 × 100 = 65%
Answer: 156 is 65% of 240
Shortcut 3 - The Unitary Method for Percentages:
If x% = y, then 1% = y/x, and 100% = (y × 100)/x
This eliminates complex calculations in competitive exams.
Exam TrapsCommon mistakes students make — avoid these
- The #1 Trap: Students confuse 'percentage of' with 'percentage more than'. For example, if A is 20% of B, it does NOT mean A is 20% more than B. '20% of B' means A = 0.20 × B. But '20% more than B' means A = B + 0.20 × B = 1.20 × B.
This confusion costs precious marks in exams.
Another frequent error is forgetting to convert percentage back to the required form. Always check if the answer needs to be in percentage, decimal, or fraction format.
Key Points to Remember
Percentage means parts per hundred, always calculated on a base value
A shopkeeper marks an item at ₹500. He gives a 20% discount. What is the selling price?
Practice 4easy
In a class of 200 students, 60% are boys. How many girls are there in the class?
Practice 5easy
A student scored 72 marks out of 120. What is the percentage of marks obtained?
Practice 6easy
The price of a book increased from ₹200 to ₹250. What is the percentage increase?
Practice 7medium
In an examination, a student scored 75% of the total marks. If the total marks are 320, how many marks did the student score?
Practice 8medium
A shopkeeper marks an item at ₹500. He offers a discount of 12% on the marked price. What is the selling price of the item?
Practice 9medium
A number is increased by 25%. If the new number is 500, what was the original number?
Practice 10medium
A product's price decreased from ₹800 to ₹600. What is the percentage decrease in price?
Practice 11medium
A student's marks increased from 60 to 75. What is the percentage increase in marks?
Practice 12medium
A shopkeeper buys an item for ₹400 and sells it at a profit of 35%. What is the selling price?
Practice 13hard
A shopkeeper marks his goods at 60% above cost price. He then offers a discount of 25% on the marked price. If the cost price of an item is ₹800, what is his profit percentage?
Practice 14hard
A number is increased by 20%, then the result is decreased by 20%. What is the net change in the original number as a percentage?
Practice 15hard
A student scored 65% in Mathematics and 72% in English. If Mathematics carries a weight of 3 and English carries a weight of 2, what is the weighted average percentage?
Practice 16hard
The price of a commodity increases by 15% in the first year and by 10% in the second year. If the original price was ₹2000, what is the price after two years?
Practice 17hard
A person's salary is increased by 25%. Later, due to economic downturn, the salary is decreased by 20%. If the final salary is ₹12,000, what was the original salary?
Practice 18hard
In an election, candidate A received 45% of votes and candidate B received 40% of votes. The remaining votes were invalid. If the total number of votes cast was 8000, how many more votes did A receive than B?
60-Second Revision — Basic Percentage
Remember: Percentage = (Part/Whole) × 100 for all basic problems
Formula: Part = (Percentage/100) × Whole for finding quantities
Trap: 'x% of y' ≠ 'x% more than y' - completely different meanings
Shortcut: Use fraction conversions (25% = 1/4) for faster calculations
Quick check: 50% should always give exactly half the original number