Finding the original percentage

Finding the original percentageExample 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 isAmount = 105% of original = 1.05 x original = £567

original = £567 1.05

= £540

Finding the original percentageAlways use the following formula :

New value = Percentage of Original value

Or

New value = Percentage x Original value

ExampleAfter 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

ExampleAn 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

ExampleDuring 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

ExampleThe 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

ExampleThe 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

ExampleThe 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

ExampleA 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

ExampleThe 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