Ratio, proportion and rates of changeKey Stage 3

Finding an original amount after a decrease

Recover the original amount before a percentage decrease.

  • The original amount is 100%. A decrease 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 discount, a price is . Find the original price.

The original amount is 100%. Subtract 15%; 85% remains. is the multiplier: 85% is 0.85 times the original amount.Divide by the multiplier to recover the original amount.
The original amount is 100%. Subtract 15%; 85% remains. is the multiplier: 85% is 0.85 times the original amount.Divide by the multiplier to recover the original amount.

Example 2

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

The original amount is 100%. Subtract 20%; 80% remains. is the multiplier: 80% is 0.8 times the original amount.Divide by the multiplier to recover the original amount.
The original amount is 100%. Subtract 20%; 80% remains. is the multiplier: 80% is 0.8 times the original amount.Divide by the multiplier to recover the original amount.

Your turn

Question 1

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

Check answer
The original amount is 100%. Subtract 12%; 88% remains. is the multiplier: 88% is 0.88 times the original amount.Divide by the multiplier to recover the original amount.
The original amount is 100%. Subtract 12%; 88% remains. is the multiplier: 88% is 0.88 times the original amount.Divide by the multiplier to recover the original amount.
Question 2

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

Check answer
The original amount is 100%. Subtract 8%; 92% remains. is the multiplier: 92% is 0.92 times the original amount.Divide by the multiplier to recover the original amount.
The original amount is 100%. Subtract 8%; 92% remains. is the multiplier: 92% is 0.92 times the original amount.Divide by the multiplier to recover the original amount.
Question 3

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

Check answer
The original amount is 100%. Subtract 25%; 75% remains. is the multiplier: 75% is 0.75 times the original amount.Divide by the multiplier to recover the original amount.
The original amount is 100%. Subtract 25%; 75% remains. is the multiplier: 75% is 0.75 times the original amount.Divide by the multiplier to recover the original amount.
Question 4

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

Check answer
The original amount is 100%. Subtract 30%; 70% remains. is the multiplier: 70% is 0.7 times the original amount.Divide by the multiplier to recover the original amount.
The original amount is 100%. Subtract 30%; 70% remains. is the multiplier: 70% is 0.7 times the original amount.Divide by the multiplier to recover the original amount.
Question 5

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

Check answer
The original amount is 100%. Subtract 6%; 94% remains. is the multiplier: 94% is 0.94 times the original amount.Divide by the multiplier to recover the original amount.
The original amount is 100%. Subtract 6%; 94% remains. is the multiplier: 94% is 0.94 times the original amount.Divide by the multiplier to recover the original amount.
← All Ratio, proportion and rates of change cardsReport a mistake