NCERT solutions for Class 8 Mathematics Chapter Proportional Reasoning–2 – complete answers & explanations

This blog provides complete NCERT solutions for Class 8 Mathematics Chapter Proportional Reasoning–2. This chapter focuses on understanding how different quantities are related through ratios and proportions in real-life situations. Students learn to solve problems involving time, money, data representation, and logical reasoning using proportional thinking. It also helps in understanding concepts like pie charts, triangle conditions, and practical applications of mathematics in daily life. In this blog, you will find clear and reliable NCERT solutions that guide students in solving questions accurately and confidently. Download the worksheet and practice alongside these solutions for better clarity and learning. You can also book a free trial now to get expert guidance and strengthen your mathematical skills.

What this NCERT chapter covers?

1. The chapter focuses on understanding proportional relationships between quantities.
2. It teaches students how to apply ratios in real-life contexts like time and money.
3. Students learn to interpret and solve data-based problems.
4. The chapter explains how to represent data using pie charts.
5. It helps students convert ratios into angles for graphical representation.
6. Students understand important geometric concepts like triangle construction.
7. The chapter introduces conditions required for forming valid triangles.
8. It develops skills to solve problems involving direct proportion.
9. Students learn to interpret charts and match data correctly.
10. It builds logical reasoning and analytical thinking skills.
11. The chapter helps in understanding assumptions in problem-solving.
12. It strengthens problem-solving techniques useful for exams and daily life.

How to use these NCERT solutions?

1. Begin by reading each question carefully from the worksheet.
2. Try solving the questions on your own before checking the answers.
3. Use the solutions to verify your answers and understand mistakes.
4. Compare your approach with the given answers to improve accuracy.
5. Focus on understanding the method used in solving problems.
6. Follow the exact order of the worksheet for better clarity.
7. Reattempt incorrect questions after reviewing the solutions.
8. Teachers and parents can guide students by explaining key concepts.
9. Practice similar problems to build confidence.
10. Use these solutions regularly for revision and exam preparation.

Important tips & tricks for students

1. Always read the question carefully before solving.
2. Pay attention to units like minutes, hours, and currency.
3. Double-check calculations to avoid small mistakes.
4. Understand the concept of proportion instead of memorising answers.
5. Practice drawing and interpreting pie charts accurately.
6. Remember rules like triangle inequality while solving geometry questions.
7. Write answers clearly and neatly to score full marks.
8. Do not skip steps in calculation-based questions.
9. Carefully follow instructions given in the question.
10. Practice regularly to improve speed and accuracy.

NCERT solutions – complete answer key

SECTION: Figure it Out 
(Page 60)

Warm-up/Cool-down = 30 minutes 
Batting = 40 minutes 
Bowling = 30 minutes 
Fielding = 50 minutes 

Hindi books = 192 
English books = 96 

₹10 coins = 40 coins → ₹400 
₹5 coins = 30 coins → ₹150 
₹2 coins = 20 coins → ₹40 
₹1 coins = 10 coins → ₹10 

Total money = ₹600

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

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)

Summer = 90° 
Rainy = 120° 
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.

(i) Yes 
(ii) No 
(iii) Yes 

Entertainment = 180° 
Sports = 90° 
News = 54° 
Information = 36° 

SECTION: Figure it Out 
(Page 65)

x = 16, y = 9 
x = 12, y = 12 
x = 36, y = 4 

SECTION: Figure it Out 
(Page 67–68)

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

Water will last for 4 days 

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

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

₹100 

SECTION: Figure it Out 
(Page 68)

(i) Walk 

(ii) 1/6 

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

(iv) Cycle and Bus 

15 hours 

3 days 

Assumption: All workers work at the same rate.

15 rows 

40 minutes 

1.2 hours (or 1 hour 12 minutes) 

49 machines 

1.5 hours 

Why NCERT solutions help students?

NCERT solutions help students build strong conceptual understanding and improve accuracy in solving problems. They guide students in writing correct answers, following proper methods, and preparing effectively for exams with confidence.

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