Crude calculation
Louise has noticed that the price of petrol has changed. Can you work out the percentage that it has increased by?
Age
14 to 16
Challenge level
Problem
When Louise had her first car, 50 litres of petrol cost £40. When she filled up the
other day, she noticed that 40 litres of petrol cost £50.
By what percentage has the cost of petrol increased over this time?
This problem is taken from the UKMT Mathematical Challenges.
Student Solutions
Answer: 56.25%
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Before 50 litres cost £40
10 litres cost £40$\div$5 = £8
Now 40 litres cost £50
10 litres cost £50$\div$4 = £12.50
125$\div$80 = 12.5$\div$8 = 1.5625 = 156.25%
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Before £40 bought 50 litres
£10 bought 12.5 litres
Now £50 buys 40 litres
£10 buys 8 litres
12.5$\div$8 = 1.5625 = 156.25%
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Before 50 litres cost £40
Now 40 litres cost £50
50 litres cost £50 + $\frac14$ of £50 = £62.50
62.5$\div$40 = 6.25$\div$4 = 1.5625 = 156.25%
Using fractions
$\frac 45$ of the amount of petrol now costs $\frac54$ of the amount
Therefore the cost has increased by $\left(\frac{5}{4}\right)^2=\frac{25}{16}$
$\frac{25}{16}\times100=156.25\%$