Percentage

Mathematics · 5 min read · Sunitha Rao

The single most useful chapter - it feeds profit & loss, interest and data interpretation.

A percentage is simply a fraction with denominator 100. Converting between fractions and percentages quickly is the real exam skill: 1/8 = 12.5%, 1/6 = 16.67%, 1/3 = 33.33%, 3/8 = 37.5%. Memorising this table turns two-minute calculations into ten-second ones.

Two ideas cover most questions. First, percentage change = (change / original) x 100, always on the original value. Second, successive percentage changes do not add up: a 10% increase followed by a 10% decrease leaves you at 99%, not 100%.

Watch the direction of comparison. "A is 25% more than B" is not the same as "B is 25% less than A" - if A is 25% more than B, then B is 20% less than A.

Important points

  • x% of y = (x/100) x y.
  • Percentage change is always calculated on the original value.
  • Successive changes of +a% and +b% give a net a + b + ab/100 percent.
  • If A is x% more than B, then B is 100x/(100+x) percent less than A.
  • Learn fraction equivalents up to 1/12 by heart.

Key formulas

Percentage change = (New - Old) / Old x 100

Net successive change = a + b + (ab/100)

Examples

  1. What is 20% of 250? (20/100) x 250 = 50.
  2. A price rises 20% then falls 20%. Net change = 20 - 20 - 400/100 = -4%, so the price is 96% of the original.
  3. A number increased by 20% becomes 96. Original = 96/1.2 = 80.

Practise Percentages questions →