Let V mL of acid and V mL of NaOH be used concentration of both acid and NaOH are same.
$\mathrm{CH}_{3} \mathrm{COOH}+\mathrm{NaOH} \rightarrow \mathrm{CH}_{3} \mathrm{COONa}+\mathrm{H}_{2} \mathrm{O}$

$\left[\mathrm{CH}_{3} \mathrm{COONa}\right]=\frac{0.1}{2}=0.05 \mathrm{M}$
Now calculate pH by hydrolysis of $\mathrm{CH}_{3} \mathrm{COONa}$
$\begin{array}{l}\mathrm{CH}_{3} \mathrm{COONa}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{CH}_{3} \mathrm{COOH}+\mathrm{NaOH} \\ {\left[\mathrm{OH}^{-}\right]=\mathrm{C} . \mathrm{h}=\sqrt{\frac{\mathrm{K}_{\mathrm{w}} \cdot \mathrm{C}}{\mathrm{K}_{a}}}=\sqrt{\frac{10^{-14} \times 0.05}{2 \times 10^{-5}}}=5 \times 10^{-6}} \\ \mathrm{p}[\mathrm{OH}]=6 \times 0.699=5.301 \\ \mathrm{pH}=[14-5.301]=8.699 \approx 8.7\end{array}$
Therefore, option (4) is the correct answer.