Login
OR
Don't worry. We'll fix this for you!
Percentage is a way to express a number as a part of 100. The word "percent" literally means "per hundred." This means when we say 25%, we mean 25 out of 100 parts. Percentages are everywhere-in calculating discounts during shopping, understanding interest rates in banks, or measuring success rates in exams.
Understanding percentages helps you compare quantities easily and solve many practical problems. Since percentages relate closely to fractions, decimals, and ratios, mastering them strengthens your overall arithmetic skills, which are crucial for competitive exams.
At its core, a percentage is a fraction with denominator 100. For example, 25% means \(\frac{25}{100}\) or 0.25 in decimal form.
To convert between fractions, decimals, and percentages:
Let's see a real-life example:
Example: What is 25% of 200 meters?
Since 25% = \(\frac{25}{100} = 0.25\), multiply 0.25 by 200 meters:
\(0.25 \times 200 = 50\) meters.
This means 25% of 200 meters is 50 meters.
There are three common types of percentage calculations:
graph TD A[Start] --> B{Type of Calculation?} B --> C[Find Percentage of Number] B --> D[Find Number from Percentage] B --> E[Calculate Percentage Increase/Decrease] C --> F[Use formula: (P/100) x N] D --> G[Use formula: (Part x 100)/P] E --> H{Increase or Decrease?} H --> I[Increase: ((New - Original)/Original) x 100] H --> J[Decrease: ((Original - New)/Original) x 100]Step 1: Identify the percentage and the number.
Percentage \(P = 15\%\), Number \(N = 500\) INR.
Step 2: Use the formula for percentage of a number:
\( \frac{15}{100} \times 500 = 0.15 \times 500 = 75 \) INR.
Answer: The discount amount is 75 INR.
Step 1: Calculate the increase.
Increase = New price - Original price = 1380 - 1200 = 180 INR.
Step 2: Use the percentage increase formula:
\[ \text{Percentage Increase} = \frac{180}{1200} \times 100 = 15\% \]
Answer: The price increased by 15%.
Step 1: Let the original price be \(x\) INR.
Step 2: Since there is a 15% discount, the selling price is 85% of the original price.
\[ 85\% \text{ of } x = 850 \implies \frac{85}{100} \times x = 850 \]
Step 3: Solve for \(x\):
\[ x = \frac{850 \times 100}{85} = 1000 \text{ INR} \]
Answer: The original price was 1000 INR.
Step 1: Use the successive percentage change formula:
\[ \text{Net Change} = \left(1 + \frac{p}{100}\right) \times \left(1 + \frac{q}{100}\right) - 1 \]
Here, \(p = 10\%\), \(q = 20\%\).
Step 2: Calculate:
\[ = (1 + 0.10) \times (1 + 0.20) - 1 = 1.10 \times 1.20 - 1 = 1.32 - 1 = 0.32 \]
Step 3: Convert to percentage:
\(0.32 \times 100 = 32\%\)
Answer: The total increase over two years is 32%.
Step 1: Assume total students = 8 parts (3 boys + 5 girls).
Boys = 3 parts, Girls = 5 parts.
Step 2: Calculate number of boys passed:
\(40\%\) of boys = \(0.40 \times 3 = 1.2\) parts.
Step 3: Calculate number of girls passed:
\(60\%\) of girls = \(0.60 \times 5 = 3\) parts.
Step 4: Total passed = \(1.2 + 3 = 4.2\) parts.
Step 5: Percentage passed = \(\frac{4.2}{8} \times 100 = 52.5\%\).
Answer: 52.5% of the class passed the exam.
When to use: When calculating percentage of a number quickly.
When to use: For quick approximations in exam conditions.
When to use: When dealing with compound percentage increases or decreases.
When to use: To avoid common calculation errors.
When to use: When converting between fractions and percentages.
Progress tracking is paywalled — subscribe to mark subtopics as understood and save your streak.
Go to practice →
Your Score
Your Rank
| Rank | Name | Score |
|---|