\(\frac{{100}}{{\frac{{100\,\,R}}{{\left( {100\,\, + \;\,R} \right)}}}}\,\, = \,\,\frac{{200}}{{40}}\,\,\,\)
\(\, \Rightarrow \,\,\frac{{100\,\, + \,\,R}}{R}\,\, = \,\,5\)
\(\,100\,\, + \;\,R\,\, = \,\,5\,\,R\,\,\) \( \Rightarrow \,\,R\,\, = \,\,\frac{{100}}{4}\,\, = \,\,25\,\Omega \)