Percentage
About 5 min · Numerical and Mathematical Ability · English
Time worked out from the lesson's 294 words at 150 words a minute, plus a minute for each question.
The word "percent" means "per hundred," so 25% literally means 25 out of 100 or 25/100. Mastering percentage is critical because it forms the foundation for profit and loss, simple interest, data interpretation, and discount problems.
Key ideas
- Percentage as a fraction: x% means x/100. To convert any fraction to percentage, multiply by 100. To convert percentage to fraction, divide by 100 and simplify.
- Percentage of a quantity: To find x% of N, calculate (x/100) × N. This is the base formula for all percentage calculations.
- Percentage change formula: Percentage change = [(New Value − Original Value) / Original Value] × 100. Positive result means increase, negative means decrease.
- Reverse percentage problem: If x% of a number is given and you need the number itself, use: Number = (Given Value × 100) / x.
- Successive percentage changes: When two percentage changes happen one after another, they don't simply add. Use the formula: Net change = a + b + (ab/100), where a and b are the two percentage changes (use negative sign for decrease).
Quick reference
- 50% = half, 25% = quarter, 20% = one-fifth — use these for mental math shortcuts
- Successive changes never simply add — always use a + b + ab/100
- To find 15%: Find 10% + 5% (half of 10%)
- Increase by x% then decrease by x% → net decrease of x²/100 %
- Reference value in comparisons = the quantity mentioned after "than"
Check yourself: 3 questions
1. A student scored 432 marks out of 600. What percentage did the student score?
2. The price of a mobile phone increased from Rs. 8,000 to Rs. 9,200. What is the percentage increase in the price?
3. If 35% of a number is 280, what is 60% of that number?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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