Substitute ${\mathrm{F}}_1=0.6125 {\mathrm{F}}_2$ into the equilibrium equation and solve for ${\mathrm{F}}_2$:

$$\begin{gathered} \sum _{}{\mathrm{M}}_{\mathrm{A}}=(0.6125) {\mathrm{F}}_2 (380 \mathrm{mm})+{\mathrm{F}}_2 (760 \mathrm{mm})-\mathrm{P}(1,520 \mathrm{mm})=0 \\ \therefore (992.75 \mathrm{mm}){\mathrm{F}}_2=\mathrm{P}(1,520 \mathrm{mm}) \end{gathered}$$