NCERT Solutions Class 8 Maths Chapter 7 Comparing Quantities Exercise 7.1

NCERT Solutions Class 8 Maths Chapter 7 Comparing Quantities Exercise 7.1 introduces students to the ideas of percentages, ratios, and fractions. This exercise will help students to understand how to convert percentages into ratios and fractions and use them to compare things. The exercise uses examples from real life such as marks obtained, price of items, and savings on goods, in a way that makes the content relevant and interesting.

These NCERT Solutions follow the latest NCERT syllabus and provide step-by-step explanations for each question. Practicing from NCERT Solutions for Exercise 7.1 strengthens students’ foundation in percentages and prepares them for more complex topics in the chapter.

1.0Download NCERT Solutions Class 8 Maths Chapter 7 Comparing Quantities Exercise 7.1 : Free PDF

Download free NCERT Solutions Class 8 Maths Chapter 7 Comparing Quantities Exercise 7.1 PDF with clear, step-by-step answers to boost your understanding and exam scores.

2.0Key Concepts in Exercise 7.1 of Class 8 Maths Chapter 7

Exercise 7.1 of Class 8 Maths Chapter 7 – Comparing Quantities focuses on foundational concepts used in comparing values, calculating percentages, and solving real-life problems involving increase or decrease in quantities. The key concepts covered in this exercise include:

• Understanding Percentages: Students will learn how to express numbers as percentages and will also learn to change from fractions to decimals and percentages, which facilitates comparison of quantities.
• Conversion of Percentages: This exercise demonstrates how to convert percentages into decimals and fractions. This is great for simplifying calculations when working through statistics.
• Application of Percentage in Real Life: Several exercise problems utilize the concept of percentage in different real life scenarios such as marks gotten, population increases, etc.
• Finding Increase or Decrease Percent: This exercise also looks at how to find out how much a quantity has increased or decreased and express that as a percent.
• Basic Ratio and Proportion Review: Since comparing quantities is essentially comparing ratios, this exercise has a built in exercise related to ratio and proportion.

3.0NCERT Class 8 Maths Chapter 7: Other Exercises

4.0NCERT Class 8 Maths Chapter 7 Exercise 7.1 : Detailed Solutions

1. Find the ratio of the following : (i) Speed of a cycle is 15 km per hour to the speed of scooter 30 km per hour. (ii) 5 m to 10 km (iii) 50 paise to ₹ 5 Sol. (i) Speed of cycle which is $15\mathrm{km}/\mathrm{hr}$ to the speed of scooter which is $30\mathrm{km}/\mathrm{hr}=15:30=1:2$. (ii) The ratio is $5\mathrm{m}:10\mathrm{km}$ or $5\mathrm{m}:10\times 10^3\mathrm{m}\left\{\because 1\mathrm{km}=10^3\mathrm{m}\right\}$ or $1:2000$. (iii) The ratio is 50 paise : ₹5 or, 50 paise : 500 paise $\{\because ₹1=100\text{ paise }\}$ or, $1:10$.
2. Convert the following ratios to percentages : (i) $3:4$ (ii) $2:3$ Sol. (i) $3:4=\frac{3}{4}\times \frac{100}{100}=\frac{3}{1}\times \frac{25}{100}=\frac{75}{100}=75\%$ (ii) Ratio $=2:3$ and percentage $=\frac{2}{3}\times 100=66\frac{2}{3}\%$
3. $72\%$ of 25 students are interested in mathematics. How many are not interested in mathematics? Mathematics. $\therefore$ Percentage of students not interested in Mathematics $=100\%-72\%=28\%$ Also, total number of students $=25$ Hence, number of students not interested in mathematics $=\frac{28}{100}\times 25=7$ students
4. A football team won 10 matches out of the total number of matches they played. If their winning percentage was 40, then how many matches did they play in all? Sol. Let x games be played in all. Since $40\%$ of the total games is given as 10 , $\therefore 40\%$ of $x=10$ $\Rightarrow \frac{40}{100}\times \mathrm{x}=10\Rightarrow \mathrm{x}=\frac{100}{40}\times 10=25$ Hence, the total games played were 25.
5. If Chameli had ₹ 600 left after spending $75\%$ of her money, how much did she have in the beginning? Sol. We know, money left with Chameli $=₹600$ $\%$ of money she spent $=75\%$ $\therefore \%$ of money left $=100\%-75\%=25\%$ Let total money in the beginning be x $\therefore 25\%$ of $\mathrm{x}=\mathrm{F}600$ or, $\frac{25}{100}\times \mathrm{x}=₹600$ or, $\mathrm{x}=₹2400$
6. If $60\%$ people in a city like cricket, $30\%$ like football and the remaining like other games, then what per cent of the people like the other games? If the total number of people are 50 lakh, find the exact number of people who like each type of game. Sol. We have, People who like cricket $=60\%$ People who like football $=30\%$ $\therefore$ People who like other games $=(100-60-30)\%=10\%$ Total number of people $=5000000$ $\therefore$ People who like cricket $=\frac{60}{100}\times 5000000=3000000=30$ lakh People who like football $=\frac{30}{100}\times 5000000=1500000=15$ lakh and, the people who like other games $=\frac{10}{100}\times 5000000=500000=5$ lakh

5.0Key Features and Benefits of Class 8 Maths Chapter 7 Exercise 7.1

• Easy Explanation of Concepts: Exercise 7.1 introduces the basics of comparing quantities using percentages, ratios, and fractions. The concepts are explained in a simple way so students can understand quickly.
• Real-Life Applications: The exercise helps students relate maths to real-life situations like discounts, profit-loss, and interest. This makes learning more practical and interesting.
• Step-by-Step Practice: The questions in this exercise allow students to build their skills step-by-step, starting from easy problems and moving to slightly tricky ones.
• Boosts Confidence: Solving this exercise improves calculation speed and helps students become more confident in solving word problems based on percentages and ratios.
• Aligned with NCERT Textbook: All topics and questions are directly based on the latest NCERT syllabus, making it perfect for school exams and revision.