Inverse Proportion (Inverse Variation) – Detailed Explanation

1. What is Inverse Proportion?

Inverse proportion (or inverse variation) describes a relationship between two quantities where if one increases, the other decreases at the same rate, and vice versa.

✅ More of one → Less of the other
✅ Less of one → More of the other

2. Formula of Inverse Proportion

If x and y are inversely proportional, their product remains constant:

x×y=k

or

y=kx​

where k is the constant of proportionality.

3. Explanation of the Formula

• When x increases, y decreases so that their product stays the same.
• When x decreases, y increases so that their product remains constant.
• This means x and y are multiplied to give a fixed number.

4. Real-Life Examples of Inverse Proportion

1. Speed and Time – If you drive faster, you take less time to reach your destination.
2. Number of Workers and Time to Complete Work – More workers finish a task in less time.
3. Length and Width of a Rectangle (for fixed area) – If you increase the length, the width decreases to keep the area the same.

5. General Rule for Solving Inverse Proportion Questions

If x₁y₁ = x₂y₂, then:

x1:x2=y2:y1​

This means:

x₁x₂=y₂y₁​​

6. Shortcut Trick (Cross Multiplication Method)

For two inversely proportional values (x₁, y₁) and (x₂, y₂):

x₁:x₂=y₂:y₁​

Multiply diagonally:

x₁×y₁ =x₂×y₂​

 Difference Between Direct and Inverse Proportion