Ratio, proportion and rates of changeKey Stage 3

Finding an original amount after an increase

Recover the original amount before a percentage increase.

  • The original amount is 100%. A increase leaves of the original amount.
  • is the multiplier: . Divide the percentage by 100 to write it as a decimal.
  • Divide the new amount by the multiplier to find the original amount.

Example 1

After a increase, a price is . Find the original price.

The original amount is 100%. Add 15%; 115% remains. is the multiplier: 115% is 1.15 times the original amount.Divide by the multiplier to recover the original amount.
The original amount is 100%. Add 15%; 115% remains. is the multiplier: 115% is 1.15 times the original amount.Divide by the multiplier to recover the original amount.

Example 2

After a increase, a price is . Find the original price.

The original amount is 100%. Add 20%; 120% remains. is the multiplier: 120% is 1.2 times the original amount.Divide by the multiplier to recover the original amount.
The original amount is 100%. Add 20%; 120% remains. is the multiplier: 120% is 1.2 times the original amount.Divide by the multiplier to recover the original amount.

Your turn

Question 1

After a increase, a price is . Find the original price.

Check answer
The original amount is 100%. Add 12%; 112% remains. is the multiplier: 112% is 1.12 times the original amount.Divide by the multiplier to recover the original amount.
The original amount is 100%. Add 12%; 112% remains. is the multiplier: 112% is 1.12 times the original amount.Divide by the multiplier to recover the original amount.
Question 2

After a increase, a price is . Find the original price.

Check answer
The original amount is 100%. Add 8%; 108% remains. is the multiplier: 108% is 1.08 times the original amount.Divide by the multiplier to recover the original amount.
The original amount is 100%. Add 8%; 108% remains. is the multiplier: 108% is 1.08 times the original amount.Divide by the multiplier to recover the original amount.
Question 3

After a increase, a price is . Find the original price.

Check answer
The original amount is 100%. Add 25%; 125% remains. is the multiplier: 125% is 1.25 times the original amount.Divide by the multiplier to recover the original amount.
The original amount is 100%. Add 25%; 125% remains. is the multiplier: 125% is 1.25 times the original amount.Divide by the multiplier to recover the original amount.
Question 4

After a increase, a price is . Find the original price.

Check answer
The original amount is 100%. Add 30%; 130% remains. is the multiplier: 130% is 1.3 times the original amount.Divide by the multiplier to recover the original amount.
The original amount is 100%. Add 30%; 130% remains. is the multiplier: 130% is 1.3 times the original amount.Divide by the multiplier to recover the original amount.
Question 5

After a increase, a price is . Find the original price.

Check answer
The original amount is 100%. Add 6%; 106% remains. is the multiplier: 106% is 1.06 times the original amount.Divide by the multiplier to recover the original amount.
The original amount is 100%. Add 6%; 106% remains. is the multiplier: 106% is 1.06 times the original amount.Divide by the multiplier to recover the original amount.
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