Percentages in Business
Growth rates, percentage points, undoing a discount, and changes that stack.
Best in your head · no pen, no calculator why?
Opens at level 2.
Lesson and untimed practice
Read the full lesson and try each skill without a clock. About 3 minutes to read.
skills · practice stats
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Percent change not tried yet
worked example
Monthly sales rise from $13,000 to $13,650. What is the percentage increase?
Answer: 5%
- Percent change = (new − old) ÷ old = ($13,650 − $13,000) ÷ $13,000 = $650 ÷ $13,000 = 5%.
- Always divide by the starting value.
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Percentage points not tried yet
worked example
A delivery firm's on-time rate falls from 46% to 40%. By how many percentage points did it fall? Give the number of points.
Answer: 6
- Percentage points are a straight subtraction of the two rates: 46 − 40 = 6 points.
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Relative change of a rate not tried yet
worked example
A repeat-customer rate moves from 20% to 22%. Relative to where it started, by what percent did it rise?
Answer: 10%
- Relative change = point change ÷ starting rate = (22 − 20) ÷ 20 = 2 ÷ 20 = 10%.
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Undo a discount not tried yet
worked example
A desk chair is on sale for $207, which is 10% off its original price. What was the original price?
Answer: $230.00
- After 10% off you pay 90% of the original, so original = $207 ÷ 0.9 = $230.
- Check: 10% of $230 is $23, and $230 − $23 = $207.
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Up then down not tried yet
worked example
A price rises 25% in March, then falls 50% in April. What is the overall percent change from the start? (Use a minus sign for a decrease.)
Answer: -37.5%
- Multiply the factors: 1.25 × 0.5 = 0.625, so the overall change is −37.5%.
- The April change is taken from the new March level, not from the start.
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