Mathematics · Class 8
Direct and Inverse Proportions
Direct and inverse variation with tables, graphs, and problems.
4 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
Direct proportion: as one quantity increases, other increases (y = kx). Inverse proportion: product constant (xy = k). Used in speed-time, workers-days, and recipe scaling.
Direct Proportion
Direct
y/x = k or y = kx
- More articles → more cost
- Graph is straight line through origin
Inverse Proportion
Inverse
xy = k
- More workers → fewer days
- Higher speed → less time for same distance
Problem Solving
Identify type first. Direct: ratio constant. Inverse: product constant.
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Direct
5 books cost ₹250. Cost of 8 books?
- 1Cost per book = 50
- 28 × 50
Answer
₹400
Example 2: Inverse
6 men finish work in 10 days. How many days for 15 men?
- 16×10 = 15×d
- 2d = 60/15
Answer
4 days
Key Points to Remember
- ✓ Check if ratio or product is constant
- ✓ Direct: y/x = k
- ✓ Inverse: xy = k
Exam Tips
- • State direct or inverse at start
- • Set up equation before solving
Practice MCQs — Direct and Inverse Proportions
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
More speed, less time for fixed distance is: