Ratio, proportion and rates of changeKS3 / GCSE

Successive percentage changes

Use percentage multipliers for repeated or successive changes.

  • For each change, start with 100%: use for an increase and for a decrease.
  • and are the individual multipliers. Multiply them to get the combined multiplier .
  • Multiply the initial amount by the combined multiplier. Keep full accuracy until the final answer.
  • Equal percentage increases and decreases do not cancel.

Example 1

A price of is increased by and then reduced by . Find the final price, to the nearest penny.

The original amount is 100%. Add 20%; 120% remains. is the multiplier: 120% is 1.2 times the original amount.The original amount is 100%. Subtract 10%; 90% remains. is the multiplier: 90% is 0.9 times the original amount. is the combined multiplier.Multiply the two multipliers.Exact value, written to 2 decimal places.

The overall change is increase.

Example 2

A price of is increased by and then reduced by . Find the final price, to the nearest penny.

The original amount is 100%. Add 20%; 120% remains. is the multiplier: 120% is 1.2 times the original amount.The original amount is 100%. Subtract 20%; 80% remains. is the multiplier: 80% is 0.8 times the original amount. is the combined multiplier.Multiply the two multipliers.Exact value, written to 2 decimal places.

The overall change is decrease.

Your turn

Question 1

A price of is increased by and then reduced by . Find the final price, to the nearest penny.

Check answer
The original amount is 100%. Add 15%; 115% remains. is the multiplier: 115% is 1.15 times the original amount.The original amount is 100%. Subtract 20%; 80% remains. is the multiplier: 80% is 0.8 times the original amount. is the combined multiplier.Multiply the two multipliers.Exact value, written to 2 decimal places.

The overall change is decrease.

Question 2

A price of is increased by and then reduced by . Find the final price, to the nearest penny.

Check answer
The original amount is 100%. Add 25%; 125% remains. is the multiplier: 125% is 1.25 times the original amount.The original amount is 100%. Subtract 15%; 85% remains. is the multiplier: 85% is 0.85 times the original amount. is the combined multiplier.Multiply the two multipliers.Keep the full value until the final step.To the nearest penny (2 decimal places).

The overall change is increase.

Question 3

A price of is increased by and then reduced by . Find the final price, to the nearest penny.

Check answer
The original amount is 100%. Add 10%; 110% remains. is the multiplier: 110% is 1.1 times the original amount.The original amount is 100%. Subtract 25%; 75% remains. is the multiplier: 75% is 0.75 times the original amount. is the combined multiplier.Multiply the two multipliers.Exact value, written to 2 decimal places.

The overall change is decrease.

Question 4

A price of is increased by and then reduced by . Find the final price, to the nearest penny.

Check answer
The original amount is 100%. Add 30%; 130% remains. is the multiplier: 130% is 1.3 times the original amount.The original amount is 100%. Subtract 10%; 90% remains. is the multiplier: 90% is 0.9 times the original amount. is the combined multiplier.Multiply the two multipliers.Exact value, written to 2 decimal places.

The overall change is increase.

Question 5

A price of is increased by and then reduced by . Find the final price, to the nearest penny.

Check answer
The original amount is 100%. Add 20%; 120% remains. is the multiplier: 120% is 1.2 times the original amount.The original amount is 100%. Subtract 10%; 90% remains. is the multiplier: 90% is 0.9 times the original amount. is the combined multiplier.Multiply the two multipliers.Exact value, written to 2 decimal places.

The overall change is increase.

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