What is Percentage & how to calculate percentage?
The word “percent” means “per hundred. or “per cent”. So, 25% means 25 out of 100 = 25/100 = 0.25.
General Formula:
Percentage = (Part / Whole) × 100
Percentage is denoted by the sign “%”
Importance of Percentage in Govt Exams
- Asked directly and indirectly in almost every competitive exam.
- Used in DI, Profit & Loss, Discount, Interest, and Mixture chapters.
- Appears in Prelims and Mains stages of exams.
- Helps in quick mental calculations.
Percentage to Fraction Conversion Table:
| Fraction | Percentage |
| 1/2 | 50% |
| 1/3 | 33.33% |
| 1/4 | 25% |
| 1/5 | 20% |
| 1/6 | 16.66% |
| 1/7 | 14.29% |
| 1/8 | 12.5% |
| 1/9 | 11.11% |
| 1/10 | 10% |
| 1/11 | 9.09% |
| 1/20 | 5% |
| 1/25 | 4% |
| 1/50 | 2% |
| 2/3 | 66.66% |
| 3/4 | 75% |
Practice and try to remember these conversions to increase your speed in solving questions asked in various Govt Jobs exams like SSC, Banking & Railway and other State Level Exams. For a more comprehensive study on the percentage and fraction conversion please read this article where we have shared the printable pdf as well as practice sheet for the same.
Important Percentage Formulas:
- Finding the Percentage of a Number:
Percentage of a number = (Value × Percentage) / 100 - Increase or Decrease by a Percentage:
New Value = Original Value × (1 ± Percentage/100) - Percentage Change Formula:
Percentage Change = (Difference / Original Value) × 100 - Successive Percentage Change Formula:
Net % change = x + y + (x × y) / 100
(Where x% and y% are two changes applied one after another)
Solved Examples
Example 1:
Q. What is 20% of 250?
A. (20 × 250) / 100 = 50
Example 2:
Q. A value is increased by 25% and then decreased by 20%. What is the overall percentage change?
A.
Net change = 25 – 20 + (25 × -20)/100 = 5 – 5 = 0%
So, no change in value.
Example 3:
Q. If 60% of a number is 120, what is the number?
A.
60% of X = 120
=> (60/100) × X = 120
=> X = (120 × 100)/60 = 200
Percentage Short Tricks for Exams
If A is what percent of B is asked:
Use formula: (A/B)*100%
Successive Increase/Decrease:
Use formula: x + y + (xy)/100
(For 20% increase and 10% decrease → 20 – 10 – (20×10)/100 = 10 – 2 = 8%)
If A is P% more than B:
Then B = A / (1 + P/100)
Quick Multiplier Method:
- Increase by 20% → multiply by 1.20
- Decrease by 25% → multiply by 0.75
Topics Where Percentage is Used:
Arithmetic is an important part of any competitive exams. There are several chapters in Arithmetic. But if you see carefully then you will notice that out of those chapters many topics are mainly based on percentage concept. So, if you can master the topic percentage then you can easily understand some more topics of Arithmetic discussed below:
| Chapter | Use of Percentage |
|---|---|
| Profit & Loss | Comparing CP and SP using percentage |
| Discount | Applying single or successive discounts |
| Interest (SI & CI) | Calculating interest rate |
| Mixture Problems | Percentage concentration or purity |
| Data Interpretation | Graphs and charts based on percentages |
Practice Tips
- Memorize common percentage-fraction values.
- Use estimation for faster solving.
- Regularly attempt timed quizzes and mock tests.
- Practice percentage-based DI sets (pie charts, tables).
Conclusion
Percentage is a scoring chapter for all government job aspirants. With just a few formulas and some practice, you can solve most questions within seconds. It is also essential for solving many arithmetic and data interpretation problems.
What to Do Next?
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