c
\(\frac{R_{1}}{R_{2}}=\frac{2}{3}\)       .....\((i)\)

\(\frac{R_{1}+10}{R_{2}}=1\)

\(\Rightarrow \quad R_{1}+10=R_{2}\)       .....\((ii)\)

\(\frac{2 \mathrm{R}_{2}}{3}+10=\mathrm{R}_{2} \quad ; \quad 10=\frac{\mathrm{R}_{2}}{3}\)

\(\Rightarrow \quad \mathrm{R}_{2}=30\, \Omega \quad \& \quad \mathrm{R}_{1}=20 \,\Omega\)

\(\frac{\frac{30 \times \mathrm{R}}{30+\mathrm{R}}}{30}=\frac{2}{3}\)

\(\mathrm{R}=60 \,\Omega\)