Percentage change · Year 10

In Year 10 you learn: reverse percentages.

Prices, populations and pay change by percentages. A multiplier turns any percentage change into a single multiplication, and working backwards (a reverse percentage) finds the amount before the change.

Key facts

  • Increase by r%: multiply by 1 + r/100 (up 15% → × 1.15).
  • Decrease by r%: multiply by 1 − r/100 (down 15% → × 0.85).
  • Percentage change = change ÷ original × 100.
  • Reverse percentage: divide the new amount by the multiplier. Never take the percentage off the new amount.
  • Successive changes: multiply the multipliers. Up 20% then down 20% is × 1.2 × 0.8 = × 0.96, a 4% decrease.
  • Percentage profit or loss uses the price paid (the cost) as the original.

Worked examples

Example 1

Increase £240 by 15%.

Answer: £276

Example 2

A bike bought for £3,200 is sold for £2,720. Find the percentage loss.

Answer: 15%

Example 3

After a 20% discount, a jacket costs £64. What was the original price?

Answer: £80

Example 4

A price rises by 25% and then falls by 20%. What is the overall change?

Answer: No overall change

Other years