3. 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 approximately what percentage has the cost of petrol increased over this time?
A $50 \%$
B $56 \%$
C $67 \%$
D $75 \%$
E $80 \%$
Solution
B

We note first that $£ 40$ is $40 \times 100$ pence, that is, 4000 pence. Therefore when Louise had her first car, the cost of petrol, in pence per litre, was
$$
\frac{4000}{50}=80 .
$$

Similarly, when she filled up the other day, the cost of petrol, in pence per litre, was
$$
\frac{5000}{40}=125 .
$$

It follows that the cost of petrol has increased by $(125-80)$ pence per litre, that is, by 45 pence per litre. As a percentage of the original price this increase is
$$
\begin{aligned}
\frac{45}{80} \times 100 & =\frac{4500}{80} \\
& =\frac{450}{8} \\
& =56 \frac{1}{4} .
\end{aligned}
$$

Therefore the increase in the cost of petrol over the given period is approximately $56 \%$.