How To Find The Original Value Before Percentage Off - BBC Bitesize

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  1. Key points
  2. Using 1% to find the original amount
    1. Examples
    2. Question
  3. Use a multiplier to find original amount
    1. Examples
  4. Practise finding the original value
    1. Quiz
  5. Real-world maths

Key points

  • Reverse percentages involves working backwards through a calculation to find the original amount (before a percentage change).

  • Understanding multipliers for increasing and decreasing by a percentage and being able to convert between decimals and percentages are important skills when calculating the original amounts.

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Using 1% to find the original amount before percentage change

To find the original value of an amount before the percentage increase/decrease:

  1. Write the amount as a percentage of the original value.

  2. Find 1% of the original value.

  3. The original value is 100%, so multiply by 100 to give the original value.

Examples

Image gallerySkip image gallery
  1. Example 1: After an increase of thirty percent a dress costs fifty-two pounds. Find the original price.
    Image caption,

    A price is increased by 30% to give £52. Find the original price.

1 of 8

Previous imageNext imageSlide 1 of 8, Example 1: After an increase of thirty percent a dress costs fifty-two pounds. Find the original price., A price is increased by 30% to give £52. Find the original price.End of image gallery

Question

A game is reduced by 15% in a sale. The sale price is £17. What was the original price?

Show answer

Work out what percentage is represented by the £17 by subtracting 15% from 100%. This is 85%. 85% of the original price is £17.

Find the value of 1% of the original price by dividing by 85. 17 ÷ 85 = 0∙2. 1% of the original price is £0∙20

Work out the original price (100%) by multiplying 1% (0∙2) by 100. 0∙2 × 100 = 20

The original price is £20

Sale price seventeen pounds after fifteen percent discount. One-hundred minus fifteen percent equals eighty-five percent. Eighty-five percent of the original price equals seventeen pounds. One percent of the original price equals seventeen divided by eighty-five equals twenty pence. The original price (one-hundred percent) equals zero point two multiplied by one-hundred equals twenty. The original price of the game was twenty pounds.
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Using a multiplier to find the original amount

To find the original amount of an amount before the percentage increase/decrease:

  1. Find the multiplier for the percentage change.

  2. Divide the amount by the multiplier.

Examples

Image gallerySkip image gallery
  1. Example 1: A value increased by thirty percent is fifty-two. Find the original amount.
    Image caption,

    A value is increased by 30% to give 52. Find the original amount.

1 of 8

Previous imageNext imageSlide 1 of 8, Example 1: A value increased by thirty percent is fifty-two. Find the original amount., A value is increased by 30% to give 52. Find the original amount.End of image galleryBack to top

Practise how to find the original value before percentage off

Practise finding the original value before percentage off with this quiz.

Quiz

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Real-world maths

A white woman looking at a trainer in a shoe shop.
Image caption, Working out the original price will show you how much you are saving on a sale item.

VAT is a tax on what you spend. It is a percentage of the cost of an item or service. Some businesses can reclaim the VAT they pay on certain items. To do this, they have to reverse the percentage increase to calculate what they are owed. The rate of VAT in the UK is currently 20%.

When shopping for clothes or shoes in a sale, the price tag might show the cost after a percentage reduction. For example, the sale price of trainers is £46 following a discount of 20%. Working out the original price will show you exactly how much you are saving in the sale.

A white woman looking at a trainer in a shoe shop.
Image caption, Working out the original price will show you how much you are saving on a sale item.
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