Answer
$R = 900\Omega$
Work Step by Step
Since same current flows through $R$ and $100\Omega$ so
$ V_{out} = I*(100\Omega) = V{in}/10 $
$\implies I = \frac{V_{in}}{1000\Omega}$
and
$ V_{out} = V_{in} - IR$
$\frac{V{in}}{10} = V_{in} - \frac{V_{in}}{1000\Omega}*R$
$\implies \frac{1}{1000\Omega}*R =\frac{9}{10} $
$\implies R = 900\Omega$
