When switch is open Resistance in upper arm & in lower arm are in series and both the series combination of resistances are parallel 
$\begin{array}{l}{\mathrm{R}}_{\mathrm{ab}}=(\mathrm{R}+2\mathrm{R})\parallel (2\mathrm{R}+\mathrm{R})\\ {\mathrm{R}}_{\mathrm{ab}}=\frac{3\mathrm{R}}{2}\end{array}$
When switch is closed
Resistances in upper arm & in lower arm are in parallel & both the parallel
combination of resistances are series
$\begin{array}{l}{\mathrm{R}}_{\mathrm{ab}}^{\mathrm{\prime }}=\mathrm{R}\parallel 2\mathrm{R}+2\mathrm{R}\parallel \mathrm{R}\\ {\mathrm{R}}_{\mathrm{ab}}^{\mathrm{\prime }}=\frac{4\mathrm{R}}{3}\\ \frac{{\mathrm{R}}_{\mathrm{ab}}}{{\mathrm{R}}_{\mathrm{ab}}^{\mathrm{\prime }}}=\frac{3\mathrm{R}}{2}\times \frac{3}{4\mathrm{R}}=\frac{9}{8}\end{array}$