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Calculating Original Prices and Values After Percentage Changes

This guide provides examples and formulas to determine original values after percentage increases or decreases. We explore scenarios like salary adjustments, sale prices, weight reductions, population growth, and house value changes. By applying the method of reversing percentage changes using simple mathematical operations, you'll learn to find the original amount before any percentage was applied. The key formula is: New value = Percentage x Original value. Master these concepts to accurately evaluate financial changes and price reductions.

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Calculating Original Prices and Values After Percentage Changes

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  1. Example This year Susan was given a 5% pay rise. If Susan earned £540 per week last year how much more will she get in her pay packet this year? Finding the original percentage Amount = 105% of 540 = 1.05 x 540 = £567 In reversing the process be aware of the mistake below that most usually make! Amount = 95% of 567 = 0.95 x 567 = £538.65 What we should have said is Amount = 105% of original = 1.05 x original = £567 original = £567 1.05 = £540

  2. Always use the following formula : Finding the original percentage New value = Percentage of Original value Or New value = Percentage x Original value

  3. Example After a pay rise of 5% Peter’s weekly pay is £126. How much did he earn before the rise? New value = Percentage x Original value Amount = 105% of original = 1.05 x original = £126 original = £126  1.05 = £120

  4. Example An electric toaster is offered in a sale at £32, after a reduction of 20%. What was the original price? Amount = 80% of original = 0.80 x original = £32 original = £32  0.8 = £40

  5. Example During a Grand Prix race, the tyres on a car are reduced in weight by 3%. If they weigh 388 kg at the end of the race, how much did they weigh at the start? Amount = 97% of original = 0.97 x original = 388 original = 388  0.97 = 400 kg

  6. Example The population of Villanova has increased by 63% during the last five years and is now 124 000. What was its population five years ago? Amount = 163% of original = 1.63 x original = 124 000 original = 124 000  1.63 = 76 073

  7. Example The price of houses in Villanova has increased by 18% during the last year. If the house costs $45 000 now, what would it have cost a year ago? Amount = 118% of original = 1.18 x original = $45 000 original = 45 000  1.18 = $38 135.59

  8. Example The purchase price of a watch is £70.50. If this includes VAT at 17½%, find the price before VAT was added. Amount = 117.5% of original = 1.175 x original = 70.50 original = 70.50  1.175 = £60

  9. Example A car, which failed its MOT test, was sold for £585, thereby making a loss of 35% on the cost price. What was the cost price? Amount = 65% of original = 0.65 x original = £585 original = 585  0.65 = £900

  10. Example The attendance of Burnley football club fell by 7% in 2001. If 2030 fewer people went to matches in 2001, how many went in 2000? Amount = 7% of original = 0.07 x original = 2030 original = 2030  0.07 = 29 000

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