$F=\left| q \right|vB\sin \theta $ $\Rightarrow \frac{{{F}_{2}}}{{{F}_{1}}}=\frac{\left| {{q}_{2}} \right|}{\left| {{q}_{1}} \right|}\times \frac{{{v}_{2}}}{{{v}_{1}}}\times \frac{{{B}_{2}}}{{{B}_{1}}}\times \frac{\sin {{\theta }_{2}}}{\sin {{\theta }_{1}}}$ $\xrightarrow[{{B}_{2}}={{B}_{1}}]{{{F}_{2}}=\frac{{{F}_{1}}}{2},{{v}_{2}}=2{{v}_{2}}}\frac{1}{2}=\left| \frac{{{q}_{2}}}{{{q}_{1}}} \right|\times 2\times 1\times \frac{\sin {{30}^{{}^\circ }}}{\sin {{120}^{{}^\circ }}}$ $\Rightarrow \left| \frac{{{q}_{2}}}{{{q}_{1}}} \right|=\frac{1}{4}\times \frac{\sin {{120}^{{}^\circ }}}{\sin {{30}^{{}^\circ }}}=\frac{1}{4}\times \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\sqrt{3}}{4}$