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October 2006 ©RSH Percentages Reverse Percentages

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October 2006 ©RSH Percentages You know how to use the MULTIPLIER to increase or decrease by a percentage. Percentages You know how to use the MULTIPLIER to increase or decrease by a percentage. Introduction Example Increase £800 by 6% Example Increase £800 by 6% Answer 106% of £800= 1.06 x 800 = £848 Answer 106% of £800= 1.06 x 800 = £848

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October 2006 ©RSH Percentages Sometimes you will need to find the original amount ! John just had a 5% pay rise, he now gets £21000 p.a. What did he get before the pay rise ? A PC costs £1024 including VAT. What does it cost before VAT is added ? Percentages Sometimes you will need to find the original amount ! John just had a 5% pay rise, he now gets £21000 p.a. What did he get before the pay rise ? A PC costs £1024 including VAT. What does it cost before VAT is added ? Introduction

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October 2006 ©RSH Percentages To work out the original, divide by the multiplier Percentages To work out the original, divide by the multiplier Notes

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October 2006 ©RSH Example John just had a 5% pay rise, he now gets £21000 p.a. What did he get before the pay rise ? Example John just had a 5% pay rise, he now gets £21000 p.a. What did he get before the pay rise ? Notes Answer Multiplier is 1.05 (5% pay rise; 100+5 = 105% = 1.05) Original = 21000 1.05 = £20000 Answer Multiplier is 1.05 (5% pay rise; 100+5 = 105% = 1.05) Original = 21000 1.05 = £20000

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October 2006 ©RSH Example During the last year, my car went down in value by 14%, it’s now worth £11550. What was it worth last year ? Example During the last year, my car went down in value by 14%, it’s now worth £11550. What was it worth last year ? Notes Answer Multiplier is 0.86 (14% reduction; 100-14 = 86% = 0.86) Original = 11550 0.86 = £13430.23 Answer Multiplier is 0.86 (14% reduction; 100-14 = 86% = 0.86) Original = 11550 0.86 = £13430.23

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October 2006 ©RSH Example Mr. Jones bought a computer for his business for £1225.00, including VAT (currently 17.5%). What was the price before VAT is added ? Example Mr. Jones bought a computer for his business for £1225.00, including VAT (currently 17.5%). What was the price before VAT is added ? Notes Answer Multiplier is 1.175 (17.5% increase; 100+17.5 = 117.5 = 1.175) Original = 1225 1.175 = £1042.55 Answer Multiplier is 1.175 (17.5% increase; 100+17.5 = 117.5 = 1.175) Original = 1225 1.175 = £1042.55 Businesses can claim the VAT back.

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October 2006 ©RSH Exercise 6696/1.08 = £6200 1)After an increase of 8%, the price of a car is £6696. Find the price of the car before the increase. 2)After a 12% pay rise, Kate’s salary was £28 560. What was her salary before the increase ? 3)Nigel’s car went down in value by 18% last year, it’s now worth £4500. How much was the car worth last year ? 4)A T.V. costs £376 including 17½ % VAT. How much did the T.V. cost before the tax was added ? 28560/1.12 = £25500 4500/0.82 = £5487.80 376/1.175 = £320

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