Explanation:
When \(100 \mathrm{mL \,HCl}\) is added to \(35 \mathrm{~mL}\) \(\mathrm{NaOH}, 35 \mathrm{mL\,\, HCl}\) is utilised to neutralise \(\mathrm{NaOH}\), while \(65 \mathrm{mL\,\, HCl}\) remains as such. Hence, the solution becomes acidic. In acid solution, the colour of methyl orange (indicator) is red due to the presence of \(\mathrm{Me}^{+}\)ions as,
\[\mathop {{\mkern 1mu} {\mkern 1mu} {\text{MeOH}}}\limits_{\begin{array}{*{20}{c}}
{{\text{Mecthyl}}{\mkern 1mu} {\text{orange}}} \\
{({\text{yellow}})}
\end{array}} \rightleftharpoons \mathop {{\text{Me}}}\limits_{{\text{Red}}}^ + \mathop { + {\text{O}}{{\text{H}}^ - }}\limits_{} \]