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JAC • Class 8 • Mathematics • Ch 10
Estimated Time: 45 Mins
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Direct and Inverse Proportions

JCERT · Class 8 · Chapter 10 · Direct and Inverse Proportions. Syllabus-aligned topic notes and teaching examples, not a complete textbook answer key.

Why This Chapter Matters

JCERT · Class 8 · Chapter 10 · Direct and Inverse Proportions. Syllabus-aligned topic notes and teaching examples, not a complete textbook answer key.

Before You Begin (Prerequisites)

  • Revise the relevant ideas from the previous grade.

What You Will Learn (Core Objectives)

  • In direct proportion, the ratioy/x is constant. In inverse proportion, the productxy is constant. Worker-time problems assume a fixed amount of work and the same constant productivity per worker.

Chapter Roadmap & Progression

1 Syllabus, textbook and notes alignm...
2 Concept and method
3 Check and common pitfall

Complete Concept Guide (100% Curriculum Coverage)

Syllabus, textbook and notes alignment

JCERT · Regular schools (Non-SOE) · Class 8 · Chapter 10 — Direct and Inverse Proportions
Official syllabus pages 152–161. Official syllabus · Prescribed Hindi book (17 chapters).

These topic notes and teaching examples are not a complete answer key to every textbook exercise. English notes use this same JCERT chapter order; a matching English textbook PDF has not been verified.

Official Hindi PDF for this exact chapter

Concept and method

In direct proportion, the ratioy/x is constant. In inverse proportion, the productxy is constant. Worker-time problems assume a fixed amount of work and the same constant productivity per worker.

Check and common pitfall

More workers need less time, so this is inverse proportion.

Key Formulas, Identities & Theorems

Key relationships
Direct:y=kx; inverse:xy=k
Observe formula conditions and units.

Conceptual Solved Examples & Case Studies

Example 1
Six equally productive workers finish a job in10days. How long will15workers take?
Step-by-Step Solution:

6×10=15×t; t=4days

More workers need less time, so this is inverse proportion.

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