How do I solve Direct and Inverse Proportions problems?

Direct proportion: when one quantity increases, the other also increases at the same rate. x/y = constant. Inverse proportion: when one quantity increases, the other decreases. x × y = constant.

What are common mistakes in Direct and Inverse Proportions?

Confusing direct and inverse proportion — always check the relationship first. Using the wrong formula for the type of proportion.

Which class covers Direct and Inverse Proportions?

Direct and Inverse Proportions is typically taught in Class 8. SparkEd has free practice for all these grades.

Where can I practise Direct and Inverse Proportions for free?

SparkEd offers free chapter-wise practice for Direct and Inverse Proportions aligned to CBSE, ICSE, and IB curricula. Visit sparkedmaths.com to start.

How to Solve Direct and Inverse Proportions — Step by Step Guide

Identify and solve problems involving direct and inverse variation. This guide covers Class 8 to 8.

Step-by-Step Method

1
Direct proportion: when one quantity increases, the other also increases at the same rate. x/y = constant.
2
Inverse proportion: when one quantity increases, the other decreases. x × y = constant.
3
For direct proportion: x₁/y₁ = x₂/y₂. Cross multiply to find the unknown.
4
For inverse proportion: x₁ × y₁ = x₂ × y₂. Solve for the unknown.
5
Real-life clue: more workers = less time (inverse), more items = more cost (direct).

Worked Example

Problem: If 6 workers can build a wall in 10 days, how many days will 15 workers take?

Solution: Inverse proportion: 6 × 10 = 15 × d. d = 60/15 = 4 days.

Common Mistakes to Avoid

✗
Confusing direct and inverse proportion — always check the relationship first.
✗
Using the wrong formula for the type of proportion.
✗
Not checking if the relationship is truly proportional (it might be neither).
✗
Forgetting units in the final answer.

Practice Direct and Inverse Proportions on SparkEd

Get free chapter-wise practice questions aligned to your board:

CBSE Class 8 Direct and Inverse Proportions

Master Direct and Inverse Proportions with Free Practice

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Frequently Asked Questions

How do I solve Direct and Inverse Proportions problems?: Direct proportion: when one quantity increases, the other also increases at the same rate. x/y = constant. Inverse proportion: when one quantity increases, the other decreases. x × y = constant.
What are common mistakes in Direct and Inverse Proportions?: Confusing direct and inverse proportion — always check the relationship first. Using the wrong formula for the type of proportion.
Which class covers Direct and Inverse Proportions?: Direct and Inverse Proportions is typically taught in Class 8. SparkEd has free practice for all these grades.
Where can I practise Direct and Inverse Proportions for free?: SparkEd offers free chapter-wise practice for Direct and Inverse Proportions aligned to CBSE, ICSE, and IB curricula. Visit sparkedmaths.com to start.

SparkEd Maths — sparked.coms@gmail.com — www.sparkedmaths.com