1. Finding the original percentage 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? 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. Finding the original percentage Always use the following formula : 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