Find the fraction which will bear the same ratio to 1/27 that 3/11 does to 5/9

Answer: Option A

$$\begin{array}{rl}& =x:\frac{1}{27}::\frac{3}{11}:\frac{5}{9}\\ & \Rightarrow \frac{5}{9}x=\frac{1}{27}\times \frac{3}{11}=\frac{1}{99}\\ & \Rightarrow x=\frac{1}{99}\times \frac{9}{5}\\ & =\frac{1}{55}\end{array}$$