Internal resistance of voltmeter is $R$.
Therefore effective resistance across $B$ and $C, R^{\prime}$ is given by
$\begin{aligned}
\frac{1}{R^{\prime}} & =\frac{1}{R}+\frac{1}{50} \\
& =\frac{50+R}{50 R}
\end{aligned}$
or $\quad R^{\prime}=\left(\frac{50 R}{50+R}\right)$
According to Ohm's law
$\begin{aligned}
V^{\prime} & =I R^{\prime} \\
\text { or } \quad \frac{100}{3} & =I \cdot\left(\frac{50 R}{50+R}\right)
\end{aligned}$

Now, total resistance of circuit
$\begin{aligned}
R^{\prime \prime} & =50+\frac{50 R}{50+R} \\
\text { or } \quad R^{\prime \prime} & =\frac{(2500+100 R)}{(50+R)}
\end{aligned}$
$\begin{array}{ll}\text { Now, } & V^{\prime \prime}=I R^{\prime \prime} \\ \Rightarrow & 100=\frac{100}{3}\left(\frac{50+R}{50 R}\right) \frac{2500+100 R}{(50+R)}\end{array}$
$\begin{array}{rlrl}\text { or } & 150 R =2500+100 R \\ \text { or } &50 R =2500 \\ \text { or } & R=50 \mathrm{k} \Omega\end{array}$