The volume of petrol that Andrea put in, as a fraction of the volume of the tank is the difference between $\frac{2}{3}$ and $\frac{1}{4}$, which is $\frac{5}{12}$, so she put in $\frac{5}{12}$ of $44$ litres and $\frac{5}{12} \times 44 = \frac{5\times 44}{12}=\frac{5\times11}{3} = \frac{55}{3}=18\frac{1}{3}$.

*This problem is taken from the UKMT Mathematical Challenges.*

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