The normality is inversely proportional to the volume of the solution.

Applying the equation,

${\mathrm{N}}_1{\mathrm{V}}_1={\mathrm{N}}_2{\mathrm{V}}_2$

given,

$$\begin{gathered} {\mathrm{N}}_1=0.5, {\mathrm{N}}_2=0.1 \\ {\mathrm{V}}_1=100 {\mathrm{cm}}^3, {\mathrm{V}}_2=? \end{gathered}$$

$$\begin{gathered} 0.5\times 100 =0.1\times {\mathrm{V}}_2 \\ {\mathrm{V}}_2=500 {\mathrm{cm}}^3 \end{gathered}$$

Therefore, the water to be added to the $100 {\mathrm{cm}}^3$ solution $=500-100=400 {\mathrm{cm}}^3$.