R
Rishtaara
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?

  1. 1Cost per book = 50
  2. 28 × 50

Answer

₹400

Example 2: Inverse

6 men finish work in 10 days. How many days for 15 men?

  1. 16×10 = 15×d
  2. 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: