Direct proportion (or direct variation) is a relationship between two quantities where if one increases, the other also increases at the same rate. Similarly, if one decreases, the other also decreases.

Understanding Direct Proportion Simply

If two things are in direct proportion:
✅ More of one means more of the other.
✅ Less of one means less of the other.

Examples:

1. Speed and Distance – If you drive faster, you cover more distance in the same time.
2. Work and Wages – More hours of work means more pay (if the rate is fixed).
3. Quantity and Cost – Buying more apples means paying more money (if price per apple is constant).

Basic Formula:

If two quantities x and y are directly proportional, they follow this relation:

xy=k

or

x=ky

where k is the constant of proportionality (a fixed number that does not change).

2. Explanation of the Formula:

• If x increases, y increases in the same ratio.
• If x decreases, y decreases in the same ratio.
• The ratio x/y always remains the same, which means their division gives a constant k.

General Rule for Solving Direct Proportion Questions

If x₁/y₁ = x₂/y₂, then:

x₁y₁=x₂y₂​​

This means:

x₁×y₂=x₂×y₁​