$V_1$ mL of NaOH of molarity X and $V_2$ mL of $\text{Ba(OH)}_2$ of molarity Y are mixed together. The mixture is completely neutralized by 100 mL of 0.1 N HCl. If $\frac{V_1}{V_2} = \frac{1}{4}$ and $\frac{X}{Y} = 4$, then what fraction of acid is neutralized by $\text{Ba(OH)}_2$?