Aqueous NaOH solution is labelled as 10% by weight mole fraction of the solute in it is

10% by weight means,

W_s= 10gm , Wt. of solution= 100gm

Wt. of solvent, W_o = 90gm

$$\begin{gathered} {\mathrm{n}}_{\mathrm{s}}=\frac{10}{40}=0.25 \mathrm{mol} \\ {\mathrm{n}}_{\mathrm{o}} = \frac{90}{18}=5 \mathrm{mol} \\ {\mathrm{X}}_{\mathrm{s}}=\frac{{\mathrm{n}}_{\mathrm{s}}}{\mathrm{n}}=\frac{0.25}{5.25}=0.0476 \end{gathered}$$