Find the fraction which will bear the same ratio to $$\frac{1}{27}$$ that $$\frac{3}{11}$$ does to $$\frac{5}{9}$$

$$\eqalign{ & = x:\frac{1}{{27}}::\frac{3}{{11}}:\frac{5}{9} \cr & \Rightarrow \frac{5}{9}x = \frac{1}{{27}} \times \frac{3}{{11}} = \frac{1}{{99}} \cr & \Rightarrow x = \frac{1}{{99}} \times \frac{9}{5} \cr & \,\,\,\,\,\,\,\,\,\,\,\, = \frac{1}{{55}} \cr} $$