How to Solve Percentage Questions Using Formula with Solved Examples
The concept of percentage questions is essential in mathematics and helps in solving real-world and exam-level problems efficiently. Mastering percentage questions enables students to tackle various arithmetic situations, handle exam questions with ease, and connect maths to daily life activities such as discounts, shopping, data analysis, and exams.
Understanding Percentage Questions
A percentage question refers to any mathematical problem where you need to calculate a "part per hundred" of a given value. This concept is widely used in percent problems, application of percentage, and comparison of data. You will often find percentage questions in topics like profit & loss, discounts, exam scores, and statistics. Understanding how to solve percentage word problems is crucial for school exams, competitive tests, and day-to-day calculations.
Formula Used in Percentage Questions
The standard formula to solve most percentage questions is:
\( \text{Percentage Value} = \dfrac{\text{Required Number}}{\text{Base Value}} \times 100 \)
To find "X% of Y":
\( X\% \text{ of } Y = \dfrac{X}{100} \times Y \)
Here’s a helpful table to understand percentage values in different contexts:
Percentage Questions Table
| Expression | Calculation | Result |
|---|---|---|
| 20% of 50 | (20/100) × 50 | 10 |
| 30% of 120 | (30/100) × 120 | 36 |
| 80% of 25 | (80/100) × 25 | 20 |
This table shows how percentage questions commonly appear in exams, assignments, and practical life.
Worked Example – Solving a Percentage Question
Let’s solve a typical percentage question step by step:
Question: A fruit seller had some apples. He sells 40% apples and still has 420 apples. What is the total number of apples he had originally?
1. Let the total apples be x.
2. Apples remaining after selling 40%: 100% − 40% = 60% of x.
3. Set up equation: 60% of x = 420
4. Convert percent to fraction: (60/100) × x = 420
5. Solve for x:
So, \(x = \frac{420 \times 100}{60}\)
\(x = 700\)
Final Answer: The fruit seller originally had 700 apples.
More Examples of Percentage Questions
Example 2: A number is decreased by 10% and then increased by 10%. The resulting number is 10 less than the original number. Find the original number.
1. Let the original number be x.
2. After 10% decrease: 0.9x
3. After 10% increase: 1.1 × 0.9x = 0.99x
4. Given: x − 0.99x = 10 → 0.01x = 10
5. So, x = 10 / 0.01 = 1000
Final Answer: The original number is 1000.
Practice Percentage Questions
Try these practice percentage questions for self-assessment:
1. What is 70% of 20?
2. By how much is 80% of 40 greater than 4/5 of 25?
3. If 20% of x = y, what is y% of 20 in terms of x?
4. If a product is first decreased by 25% and then increased by 20%, what is the net percentage change?
Common Mistakes to Avoid
- Mixing up percentage increase with percentage decrease calculations.
- Forgetting to convert percentage to decimals or fractions before multiplying.
- Not completing all calculation steps, leading to errors in word problems.
- Incorrectly applying the order of operations in multi-step percentage questions.
Real-World Applications
The concept of percentage questions is everywhere: calculating marks, estimating discounts, managing budgets, analysing data, and preparing for exams like SAT and CBSE boards. Vedantu makes learning easier by linking these percentage questions to your school syllabus and real-life situations so you are well-prepared for all challenges.
Page Summary
We explored the idea of percentage questions, formulas used, and various examples. You have learned how to solve step-by-step problems, avoid common mistakes, and connect the concept to practical uses. Keep practising percentage questions regularly on Vedantu to build your confidence.
Related Topics and Further Learning
- Percentage – Learn core percentage concepts and calculations.
- Profit Loss Percentage – Apply percentages to profit and loss problems.
- Fraction to Percent – Understand how to convert between fractions and percentages.
- Percentage Increase Decrease – Study percentage change problems for exams.
- Comparing Quantities Using Percentage – Master comparison-based questions in exams.
- Ratio to Percentage – Learn to convert ratios to percentages.
- How to Calculate Percentage – Get direct help for calculation methods.
- Application of Percentage – Explore practical and exam-based examples.
- Percentage Error – Learn accuracy and error calculations in exams.
FAQs on Percentage Questions Explained with Concepts and Problem Solving Methods
1. What is a percentage in maths?
A percentage is a number expressed as a fraction out of 100. The word percent means “per hundred,” so 45% means 45 out of 100.
- 50% = 50/100 = 0.5
- 25% = 25/100 = 0.25
- 100% represents a whole quantity
2. How do you calculate percentage of a number?
To calculate the percentage of a number, multiply the number by the percentage written as a fraction or decimal. The formula is (Percentage/100) × Number.
- Find 20% of 150
- = (20/100) × 150
- = 0.2 × 150
- = 30
3. What is the formula to calculate percentage?
The basic percentage formula is (Part/Whole) × 100. It helps find what percent one quantity is of another.
- If a student scores 45 out of 60:
- Percentage = (45/60) × 100
- = 0.75 × 100
- = 75%
4. How do you convert a fraction into a percentage?
To convert a fraction to a percentage, multiply the fraction by 100%.
- Example: Convert 3/4 into percentage
- (3/4) × 100 = 75
- Answer = 75%
5. How do you convert a decimal into a percentage?
To convert a decimal to a percentage, multiply the decimal by 100 and add the percent sign.
- Example: 0.65 × 100 = 65%
- Example: 0.08 × 100 = 8%
6. What is percentage increase and how do you calculate it?
A percentage increase shows how much a value has grown compared to its original value. The formula is ((Increase ÷ Original Value) × 100).
- Original price = 200
- New price = 250
- Increase = 50
- (50/200) × 100 = 25%
7. What is percentage decrease and how is it calculated?
A percentage decrease shows how much a value has reduced compared to its original value. The formula is ((Decrease ÷ Original Value) × 100).
- Original value = 500
- New value = 400
- Decrease = 100
- (100/500) × 100 = 20%
8. How do you calculate percentage profit or loss?
Percentage profit or loss is calculated using cost price and selling price.
- Profit % = (Profit ÷ Cost Price) × 100
- Loss % = (Loss ÷ Cost Price) × 100
- Cost Price = 800, Selling Price = 1000
- Profit = 200
- (200/800) × 100 = 25% profit
9. What is the difference between percentage and percent?
The word percent means “per hundred,” while percentage refers to the calculated value expressed per hundred.
- “60 percent” describes a ratio
- “The percentage is 60%” describes the result
10. What are common mistakes in solving percentage questions?
Common mistakes in percentage questions usually involve incorrect base values or formula misuse.
- Forgetting to divide by 100
- Using wrong original value in percentage increase or decrease
- Confusing profit percentage with profit amount
- Not converting percentages to decimals correctly
