Fraction and percentage - WJECFurther examples for Intermediate and Higher tier

Example 1

Barry bought a brand new car in 2009. It cost him £16,000. Its value decreased by 8% every year and in 2014 he decided to sell it. How much was it worth then? Give your answer to the nearest pound.

Solution

There are a couple of ways you can work this out. One is by using powers, and you can find out how to do this in the Percentage change guide. Another method, which is a bit more time consuming, is as follows:

We will work to the nearest penny and round at the end to the nearest pound:

• Decrease is 8%, so multiplier is 0.92 as 100% − 8% = 92%
• 2010 value = 0.92 × £16,000 = £14,720
• 2011 value = 0.92 × £14,720 = £13,542.40
• 2012 value = 0.92 × £13,542.40 = £12,459.008 = £12,459.01 (nearest penny)
• 2013 value = 0.92 × £12,459.01 = £11,462.2892 = £11,462.29 (nearest penny)
• 2014 value = 0.92 × £11,462.29 = £10,545.3068 = £10,545.31 (nearest penny) = £10,545 (nearest pound)

Example 2

In a sale a tent was reduced each day by ¼ until it was sold. It was originally priced £140. It was sold after four days. How much did it sell for? Give your answer to the nearest penny.

Solution

Each day the reduction is ¼, so we will work out 1 – ¼ = ¾ of the previous price each time.

• At start price = £140
• Day 1 price = ¾ × £140 = £105
• Day 2 price = ¾ × £105 = £78.75
• Day 3 price = ¾ × £78.75 = £59.0625 = £59.06 (to nearest penny)
• Day 4 price = ¾ × £59.06 = £44.295 = £44.30 (to nearest penny)