NCERT Solutions for Class 8 Maths Chapter 3 Proportional Reasoning 2

This worksheet provides complete and accurate NCERT Solutions for Class 8 Mathematics Chapter Proportional Reasoning–2. This chapter helps students understand how quantities are related through ratios, proportions, and real-life situations like time distribution, money calculation, and data representation. It is an important chapter because it builds logical thinking and strengthens problem-solving skills, which are essential for higher-level mathematics. This worksheet follows the NCERT pattern and ensures that students get clear and reliable answers for better understanding and revision.

Chapter summary: stories, poems & themes

This NCERT Chapter Proportional Reasoning–2 is mainly activity-based and focuses on numerical and real-life problem solving. The worksheet includes different types of questions such as time allocation, money calculation, pie charts, ratios, and proportional reasoning situations. Students learn how to interpret data, work with angles in pie charts, and apply mathematical logic in everyday contexts. The chapter emphasizes understanding relationships between quantities rather than memorizing formulas.

What this NCERT chapter covers?

• Understanding proportional reasoning through real-life examples 
• Working with ratios and comparing quantities 
• Interpreting and creating pie charts using angles 
• Solving problems related to time, money, and data 
• Logical reasoning using mathematical relationships 
• Observation-based and activity-based learning 

How to use these NCERT solutions?

Students should first try to solve all questions in this worksheet on their own. After attempting, they can use these NCERT Solutions to check their answers and understand the correct method. Parents and teachers can guide students using these solutions to explain concepts clearly. The answers are arranged in the same order as given in the worksheet, which makes it easy to follow and revise. This approach helps students build confidence and improve accuracy.

Student tips & learning tricks

• Always read the question carefully and identify what is being compared 
• Convert ratios into simple forms before solving 
• While working with pie charts, remember that the total is 360° 
• Check calculations step by step to avoid mistakes 
• Understand the logic behind answers instead of memorizing 
• Pay attention to assumptions mentioned in questions 

Why NCERT solutions are important?

NCERT Solutions are important because they follow the exact curriculum and help students understand concepts clearly. They build a strong foundation in mathematics and improve problem-solving skills. These solutions also help students prepare better for school exams and assessments. By practicing regularly, students gain confidence and develop accuracy in solving questions.

Complete answer key – NCERT solutions

SECTION: Figure it Out (Page 60)

1. Warm-up/Cool-down = 30 minutes 
2. Batting = 40 minutes 
3. Bowling = 30 minutes 
4. Fielding = 50 minutes 

5. Hindi books = 192 
6. English books = 96 

7. ₹10 coins = 40 coins → ₹400 
8. ₹5 coins = 30 coins → ₹150 
9. ₹2 coins = 20 coins → ₹40 
10. ₹1 coins = 10 coins → ₹10 
Total money = ₹600 

11. No, all triangles will not be congruent because they can have different sizes even if the ratio of sides is the same. 

12. No, a triangle cannot be constructed because the sum of two sides (1 + 3 = 4) is less than the third side (5). 

SECTION: Figure it Out (Page 62)

1. Summer = 90° 
2. Rainy = 120° 
3. Winter = 150° 

Explanation: 
Collect data of students’ favourite subjects, convert them into ratios, and then convert into angles out of 360° to draw the pie chart. 

4. (i) Yes 
(ii) No 
(iii) Yes 

5. Entertainment = 180° 
6. Sports = 90° 
7. News = 54° 
8. Information = 36° 

SECTION: Figure it Out (Page 65)

1. x = 16, y = 9 
2. x = 12, y = 12 
3. x = 36, y = 4 

SECTION: Figure it Out (Page 67–68)

1. (i) Yes 
(ii) Yes 
(iii) No 
(iv) Yes 
(v) No 
(vi) Yes 

2. Water will last for 4 days 

Assumption: Each family uses the same amount of water daily. 

3. Answers based on chart: 
(Use appropriate matching as per chart) 

4. ₹100 

SECTION: Figure it Out (Page 68)

5. (i) Walk 

6. (ii) 1/6 

7. (iii) Total children = 108 
Children using taxi = 18 

8. (iv) Cycle and Bus 

9. 15 hours 

10. 3 days 

Assumption: All workers work at the same rate. 

11. 15 rows 

12. 40 minutes 

13. 1.2 hours (or 1 hour 12 minutes) 

14. 49 machines 

15. 1.5 hours 

Strengthen your understanding of Class 8 Mathematics with accurate NCERT Solutions and build a strong foundation in proportional reasoning concepts.

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