Percentage: Percentage Decrease

Concept Explanation

When a quantity reduces by x%, the new value is (100 − x)% of the original, or original × (1 − x/100).

Formula

New value = Original × (1 − P/100). Decrease amount = Original × (P/100).

Finding Original from Decreased Value

If a P% decrease gives new value N, then Original = N × 100/(100 − P).

Finding Percentage Decrease

Decrease % = ((Old − New)/Old) × 100. Always divide by the original value.

Common Trap

A 20% drop from 500 gives 400, but a 20% rise from 400 gives 480, not 500. Increase and decrease percentages are not reversible unless the base is the same.