Find the fraction which bears the same ratio to $$\frac{1}{{27}}$$ that $$\frac{3}{7}$$ does to $$\frac{5}{9}$$ = ?

$$\eqalign{ & {\text{Let the fraction is }}x \cr & \Rightarrow x:\frac{1}{{27}}::\frac{3}{7}:\frac{5}{9} \cr & \Rightarrow \frac{x}{{\frac{1}{{27}}}} = \frac{{\frac{3}{7}}}{{\frac{5}{9}}} \cr & \Rightarrow 27x = \frac{{3 \times 9}}{{7 \times 5}} \cr & \Rightarrow x = \frac{1}{{35}} \cr} $$