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Chapter 10: Direct and Inverse Proportions

    Introduction

    Direct Proportion

    Inverse Proportion

    Compound Proportion

    Exercise 10.1

    Exercise 10.2

    Exercise 10.3

    Exercise 10.4

    What We Have Discussed?

    Easy Level Worksheet

    Moderate Level Worrksheet

    Hard Level Worksheet

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Chapter 10: Direct and Inverse Proportions > Compound Proportion

Compound Proportion

Compound proportion involves multiple quantities that are either directly or inversely proportional to another quantity. In other words, it's a situation where one quantity depends on two or more other quantities, and these relationships can be either direct or inverse.

When solving problems involving compound proportion, we need to:

(1) Identify how each quantity affects the main quantity we're solving for

(2) Determine whether each relationship is direct or inverse

(3) Apply all these relationships together to solve the problem

Types of Relationships in Compound Proportion

Multiple Direct Proportions: When a quantity increases or decreases based on multiple directly proportional relationships. For example, if the amount of work done is proportional to both the number of workers and the number of hours worked.

Multiple Inverse Proportions: When a quantity changes based on multiple inversely proportional relationships. For example, if the time taken to fill a tank is proportional to both the number of pipes and their width.

Mixed Proportions: When some quantities are directly proportional while others are inversely proportional to the main quantity. For example, if the time taken to complete a job is proportional to the amount of work but proportional to the number of workers.

If y is the dependent variable and x₁, x₂, x₃ are independent variables, then:

For direct proportion: y ∝

For inverse proportion: y ∝

For compound proportion: y ∝ (x₁ × x₂)/x₃ (where x₁ and x₂ are , x₃ is )

Compound proportion is commonly found in scenarios involving:

  • Work and time problems

  • Speed, distance, and time relationships

  • Manufacturing and production rates

  • Resource allocation

  • Construction projects