Core ConceptRead this first — the foundation of the topic
Percentage change is the difference between the original value and the new value, expressed as a percentage of the original value. This concept appears in almost every SSC CGL paper and forms the backbone of profit-loss, simple interest, and data interpretation questions. Core Concept: When any quantity increases or decreases, we calculate the percentage change to measure the rate of change. For example, if your salary increases from Rs 20,000 to Rs 25,000, the percentage increase is 25%.
Formula BlockMemorise — at least one formula appears in every paper
Block:
• Percentage Increase = [(New Value - Original Value) / Original Value] × 100
• Percentage Decrease = [(Original Value - New Value) / Original Value] × 100
• New Value after x% increase = Original Value × (100 + x)/100
• New Value after x% decrease = Original Value × (100 - x)/100
• Successive percentage changes: If a value changes by a% then b%, final change = [a + b + (ab/100)]%
Exam PatternsWhat examiners ask — read before attempting PYQs
SSC loves asking percentage change in population growth, salary hikes, price fluctuations, and successive discounts. Questions often involve finding original values when final values and percentage changes are given.
ShortcutsUse these to save 30–60 seconds per question
1
Two successive increases of x% = (x + x + x²/100)% total increase
2
One increase of x% followed by decrease of x% = (x²/100)% net decrease
3
25% increase means multiply by 1.25
4
20% decrease means multiply by 0.8
5
12.5% increase means multiply by 9/8
Worked ExampleSolve this step-by-step before moving on
1
Step 1
Identify original value = 50,000, new value = 65,000
2
Step 2
Find increase = 65,000 - 50,000 = 15,000
3
Step 3
Apply formula = (15,000/50,000) × 100 = 30%
Answer: 30% increase
Worked Example 2:
A number is first increased by 20% and then decreased by 15%. Find the overall percentage change.
1
Step 1
Let original number = 100 (always take 100 for easier calculation)
2
Step 2
After 20% increase = 100 × 1.2 = 120
3
Step 3
After 15% decrease = 120 × 0.85 = 102
4
Step 4
Overall change = 102 - 100 = 2
5
Step 5
Percentage change = 2% increase
Alternative: Using formula = 20 + (-15) + (20×(-15)/100) = 20 - 15 - 3 = 2% increase
Shortcut Trick #3: Percentage to fraction conversions:
• 12.5% = 1/8, 16.67% = 1/6, 33.33% = 1/3, 66.67% = 2/3
• These help in quick mental calculations during exams.
Exam TrapsCommon mistakes students make — avoid these
#1: Students often confuse which value to use as base. Remember: percentage change is always calculated on the ORIGINAL value, not the new value. If price changes from Rs 100 to Rs 120, the base is Rs 100, not Rs 120.
Many students calculate (20/120) × 100 instead of (20/100) × 100, leading to wrong answers.
Exam Strategy: Practice reverse calculations where you find original values from final values and percentage changes. SSC frequently tests this concept in tricky word problems involving multiple successive changes.
Key Points to Remember
Percentage change = [(New Value - Original Value) / Original Value] × 100
Always use original value as denominator, never the new value
Successive changes formula: a + b + (ab/100) for changes of a% and b%
The price of a book increased from ₹200 to ₹250. What is the percentage increase in price?
Practice 2easy
A shopkeeper reduced the price of a shirt from ₹800 to ₹600. What is the percentage decrease?
Practice 3easy
The salary of an employee increased by 15%. If the new salary is ₹11,500, what was the original salary?
Practice 4easy
The population of a town decreased by 20% in one year. If the population is now 32,000, what was the population one year ago?
Practice 5easy
A number is increased by 25% and then decreased by 20%. What is the net percentage change?
Practice 6easy
The cost price of an item is ₹500. If it is sold at a 30% profit, what is the selling price?
Practice 7medium
A shopkeeper buys an item for ₹800. He marks it up by 50% and then offers a discount of 30% on the marked price. What is his profit or loss percentage?
Practice 8medium
A student's marks increased from 60 to 75. What is the percentage increase in marks?
Practice 9medium
The value of a car depreciates by 15% in the first year and by 10% in the second year. If the initial value was ₹5,00,000, what is the value after two years?
Practice 10medium
The price of a commodity increases by 25% in the first year and then decreases by 20% in the second year. What is the net percentage change in price over the two years?
Practice 11medium
A product's price is increased by 20%, and then the new price is decreased by 25%. What is the net percentage change in the original price?
Practice 12hard
A shopkeeper increases the price of an item by 25%, then due to poor sales, reduces the new price by 20%. If the final price is ₹600, what was the original price?
Practice 13hard
A worker's salary increases by 15% in Year 1 and by 12% in Year 2. If his salary after Year 2 is ₹64,400, what was his original salary?
Practice 14hard
A merchant buys goods at ₹80 per unit. He marks up the price by 50%, then offers a discount of 30% on the marked price. What is his profit/loss percentage?
Practice 15hard
A product's price is increased by 25%. To bring it back to the original price, by what percentage should the new price be reduced?