NCERT Solutions for Class 8 Mathematics Ganita Prakash Part II Chapter 1
NCERT solutions for Class 8 Mathematics Chapter Fractions in disguise – complete answers & explanations
In this chapter of Class 8 Mathematics, titled "Fractions in Disguise," students explore how fractions, decimals, and percentages are interconnected. The chapter focuses on understanding how to convert fractions to percentages, interpret percentage changes, and solve real-world problems involving percentages. By learning these concepts, students will be able to tackle problems related to profit, loss, interest rates, and population growth. Download the worksheet and practice alongside solutions for better clarity. Book a free trial now to get expert guidance.
What this NCERT chapter covers?
1. Understanding fractions as percentages and
learning to convert fractions to percentages.
2. Expressing percentages as fractions and decimals.
3. Solving problems involving percentage increase or decrease in different contexts.
4. Calculating percentage profit and loss in transactions, including tax and discount scenarios.
5. Learning about growth and compounding, including simple and compound interest calculations.
6. Using percentages to describe change, such as population growth or price changes over time.
How to use these NCERT solutions?
1. Students should first attempt the
questions in the worksheet to practice and then compare their answers with the provided solutions.
2. After attempting the questions, use the solutions to understand the correct methods and approaches for solving percentage-related problems.
3. Parents and teachers can guide students through examples, ensuring they understand each concept, such as calculating percentage profit or handling compound interest.
4. The solutions follow the worksheet order exactly, making it easy to cross-check each question.
Important tips & tricks for students
1. When converting fractions to percentages, multiply by 100 and add the percentage symbol (%).
2. For problems involving percentage increase or decrease, always compare the final value with the initial value.
3. In profit and loss calculations, compare the selling price to the cost price to determine profit or loss.
4. Practice using mental math and estimation to quickly calculate common percentages like 10%, 20%, 25%, and 50%.
5. For compounded growth, remember that the interest is calculated on the new principal at each step.
NCERT solutions – complete answer key
1.1 Fractions as Percentages
1. Example 1: Surya mixes red and yellow paints. What percentage of the colour is red?
Answer: 75% of the colour is red, as 3/4 of the mixture is red.
2. Example 2: Surya wants to save 2/5 of his money for a new canvas. What percentage is that?
Answer: 40% of his money is saved for the canvas.
1.2 Percentage of Some Quantity
1. Madhu ate 120 g of biscuits with 25% sugar. How much sugar did she eat?
Answer: Madhu ate 30 g of sugar.
2. Madhav ate 95 g of biscuits with 35% sugar. How much sugar did he eat?
Answer: Madhav ate 33.25 g of sugar.
1.3 Using Percentages to Compare Proportions
1. Example 1: Eesha scored 42 out of 50 in English and 70 out of 80 in Science. Which is better?
Answer: Eesha scored 84% in English and 87.5% in Science, so she performed better in Science.
1.4 Percentage Increase or Decrease
1. Example 2: The price of tomatoes increased from ₹30 to ₹42. What is the percentage increase?
Answer: The percentage increase is 40%.
2. Example 3: The footfall in a theater decreased from 160 to 100 after COVID. What is the percentage decrease?
Answer: The percentage decrease is 37.5%.
1.5 Profit and Loss
1. Kishanlal bought sweaters for ₹300 and sold them for ₹430. What is his profit percentage?
Answer: The profit percentage is 43.33%.
2. Raghu sold 10 kg of rice at a loss of ₹50. What is the percentage loss?
Answer: The percentage loss is 14.28%.
1.6 Growth and Compounding
1. Example 7: If ₹6000 is invested at an interest rate of 10% for 3 years without compounding, what is the total amount after 3 years?
Answer: The total amount after 3 years is ₹7800.
2. Example 8: If ₹6000 is invested with compounding, what is the total amount after 3 years?
Answer: The total amount after 3 years with compounding is ₹7986.
1.7 Decline
1. Example 10: A TV is bought for ₹21,000 and depreciates by 5%. What is the value after one year?
Answer: The value of the TV after one year is ₹19,950.
2. Example 11: The population of a village is decreasing by 10% every decade. What is the population after 3 decades?
Answer: The population after 3 decades is approximately 910.
Figure it Out
1. Bengaluru's population in 2025 is 250% of its 2000 population. If the population in 2000 was 50 lakhs, what is the population in 2025?
Answer: The population in 2025 is 125 lakhs.
2. The mobile phone price is ₹8250. What is the final price after an 18% GST?
Answer: The final price is ₹9720.
Why NCERT solutions help students?
NCERT solutions help students understand percentage-related concepts in a clear, structured manner. With step-by-step explanations, these solutions build conceptual clarity and improve problem-solving skills, especially for real-world applications like profit calculation, price changes, and interest rates.
Help your child build strong Mathematics fundamentals with expert-guided learning support.