🗺️ Chapter Roadmap
1 What is a Percentage?
The word "Percent" is made of two parts: Per (Meaning "For every") and Cent (Meaning "100"). So, Percentage simply means "Out of 100". Its mathematical symbol is %.
The Basic Concept
If you score 40 marks out of a total 100 marks in a test, your result is exactly 40%.
2 Golden Conversions to Memorize
To save precious time in competitive exams, you must memorize these common fraction-to-percentage conversions. Don't calculate them every time!
3 The Zero-Cutting Trick (Speed Math)
If you need to find something like "30% of 40", do not use long multiplication. Simply cut one zero from the percentage and one zero from the number, then multiply what is left.
⚡ Speed Math Examples:
- 30% of 40 → 3 × 4 = 12
- 70% of 90 → 7 × 9 = 63
- 20% of 150 → 2 × 15 = 30
*Note: This trick works perfectly whenever both numbers end with at least one zero.*
4 The Magic Swap Trick
This is a secret trick that examiners don't tell you. Percentages are reversible! x% of y is exactly the same as y% of x.
Exam Question: Find 16% of 50 without a calculator.
Finding 16% of 50 is difficult.
BUT wait... let's swap the numbers!
Instead, calculate 50% of 16.
We know 50% just means "half".
Half of 16 is 8.
(So, 16% of 50 is also 8!)
5 Percentage Increase/Decrease Formula
If a price goes up or down, how do you find the percentage of that change? Just memorize this simple formula:
The Golden Formula
(Difference divided by Original Value, then multiply by 100)
The price of a shirt increased from Rs. 500 to Rs. 600. What is the percentage increase?
- First, find the difference (Change): 600 - 500 = 100
- Put it in the formula: 100500 × 100
- Solve it: 15 × 100 = 20%
Answer: 20% Increase