The ratios $\frac{3a5b}{36}$ and $\frac{4c7d}{45}$ are positive integers if $3a5b$ is divisible by $36$ (hence by $4$ and $9$) and $4c7d$ is divisible by $45$ (hence by $5$ and $9$).

$3a5b$ is divisible by $36$ if the last digit is $2$ or $6$ and because $3a5b$ is divisible by $9$ the only two possible cases are $\frac{3456}{36} = 96$ and $\frac{3852}{36} = 107$.

$4c7d$ is divisible by $45$ if the last digit is $0$ or $5$ and because $4c7d$ is divisible by $9$ the only two possible cases are $\frac{4275}{45} = 95$ and $\frac{4770}{45} = 106$.

Now we obtain the desired ordering $\frac{4275}{45} < \frac{3456}{36} < \frac{4770}{45} < \frac{3852}{36}$.