which is the greatest ratio of following 3:4 , 5:7 ,9:11 ,1:8

The given ratios are 3 : 4; 5 : 7; 9 : 11 and 1 : 8.
Which can be rewritten as $\frac{3}{4}; \frac{5}{7}; \frac{9}{11} \mathrm{and} \frac{1}{8}$.
To find the greatest number, we have to first find the L.C.M. of their denominators as;

$2\times 2\times 1\times 7\times 11\times 2 =616$
Now we make the denominators of all given rational numbers same as;
$$\begin{gathered} \frac{3}{4}\times \frac{154}{154} = \frac{462}{616} \\ \frac{5}{7}\times \frac{88}{88} = \frac{440}{616} \\ \frac{9}{11}\times \frac{56}{56} = \frac{504}{616}\frac{1}{8}\times \frac{77}{77} = \frac{77}{616} \end{gathered}$$
So the greatest rational number is $\frac{504}{616}$ i.e. $\frac{9}{11}$.
Therefore the greatest ratio is 9 : 11.