How to Solve Percentage Word Problems for Exams and Homework
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: Stepwise Practice and Solutions
1. What is a percentage question?
A percentage question is a math problem that involves calculating a part of a whole expressed as a fraction of 100. These questions commonly ask to find the percentage value, percentage increase or decrease, or convert numbers between fractions, decimals, and percentages. Understanding how to solve these is essential for exams like CBSE and competitive tests.
2. How do you solve percentage word problems?
To solve percentage word problems, follow these steps:
1. Identify the total or base value.
2. Convert the percentage into a decimal by dividing by 100.
3. Multiply the base value by the decimal percentage.
4. Interpret the result in the context of the problem.
Using clear, step-by-step calculations helps in solving exam and class examples effectively.
3. Can I get a PDF of percentage questions with solutions?
Yes, percentage questions with solutions PDF are available for download to practice offline. These resources include solved examples, practice sets for different grades, and exam-oriented questions with step-wise solutions, aligning with the CBSE and other syllabus standards.
4. What is 80% of 25 in a question?
To find 80% of 25, multiply 25 by 80 and then divide by 100: (80 × 25) ÷ 100 = 20. This calculation shows that 80% of 25 equals 20, which is a basic percentage problem commonly asked in exams.
5. Are percentage questions important for SAT or board exams?
Yes, percentage questions are an important part of the syllabus in both SAT and board exams like CBSE. They test fundamental arithmetic skills, real-life problem-solving ability, and are frequently included in competitive exams, making clear understanding and practice essential for success.
6. Why do students confuse percentage increase and percentage decrease in word problems?
Students often confuse percentage increase and percentage decrease because both involve changing values but in opposite directions. Remember:
• Percentage increase adds to the original value.
• Percentage decrease subtracts from the original value.
Careful reading and noting whether the problem mentions rise or reduction help avoid this confusion.
7. How can I avoid calculation mistakes in percentage questions?
To avoid mistakes in percentage calculations:
1. Write all steps clearly and avoid skipping intermediate values.
2. Double-check percentage conversions (e.g., 25% as 0.25).
3. Use brackets appropriately in calculations.
4. Practice with varied problems to build accuracy.
These practices reduce errors and help in board and competitive exam settings.
8. Why is it important to show steps in percentage answers?
Showing step-wise solutions is important because:
• It demonstrates clear understanding of percentage concepts.
• Helps teachers award partial marks in exams.
• Makes it easier to identify and correct mistakes.
• Builds confidence and clarity during problem-solving.
Always write neat steps for better exam performance.
9. What types of mistakes lower marks in percentage question exams?
Common mistakes that reduce marks include:
• Incorrect conversion of percentages to decimals or fractions.
• Skipping calculation steps causing loss of partial credit.
• Misreading the problem’s percentage direction (increase vs decrease).
• Rounding errors without proper justification.
Careful attention and practice help avoid these errors.
10. Why do exam questions use unusual numbers in percentage problems?
Examiners often use unusual numbers in percentage questions to:
• Test students’ conceptual understanding beyond simple cases.
• Encourage application of formulas and problem-solving methods.
• Avoid rote memorization and promote critical thinking.
Practice with varied and complex values to perform well in exams.
