A reactant (A) from two products :

$\text{A\hspace{0.17em}}\stackrel{{\text{k}}_{\text{1}}}{\to }{\text{\hspace{0.17em}B,\hspace{0.17em}Activation\hspace{0.17em}Energy\hspace{0.17em}Ea}}_{\text{1}}$

$\text{A\hspace{0.17em}}\stackrel{{\text{k}}_{\text{2}}}{\to }{\text{\hspace{0.17em}C,\hspace{0.17em}Activation\hspace{0.17em}Energy\hspace{0.17em}Ea}}_{\text{2}}$

${\text{If\hspace{0.17em}Ea}}_{\text{2}}{\text{\hspace{0.17em}=\hspace{0.17em}2\hspace{0.17em}Ea}}_{\text{1}}{\text{,\hspace{0.17em}then\hspace{0.17em}k}}_{\text{1}}{\text{\hspace{0.17em}and\hspace{0.17em}k}}_{\text{2}}\text{\hspace{0.17em}are\hspace{0.17em}related\hspace{0.17em}as\hspace{0.17em}:}$

            

            

${\text{k}}_{\text{1}}{\text{\hspace{0.17em}=\hspace{0.17em}A}}_{\text{1}}{\text{e}}^{{\text{-E}}_{{\text{a}}_{\text{1}}}\text{/RT}}\mathrm{....}\left(\text{i}\right)$

${\text{k}}_{\text{2}}{\text{\hspace{0.17em}\hspace{0.17em}A}}_{\text{2}}{\text{e}}^{{\text{-E}}_{{\text{a}}_{\text{2}}}\text{/RT}}\mathrm{....}\left(\text{ii}\right)$

On dividing eqn (i) from eqn. (ii)

$\frac{{\text{k}}_{\text{1}}}{{\text{k}}_{\text{2}}}\text{\hspace{0.17em}=\hspace{0.17em}}\frac{{\text{A}}_{\text{1}}}{{\text{A}}_{\text{2}}}({\text{E}}_{{\text{a}}_{\text{2}}}-{\text{\hspace{0.17em}E}}_{{\text{a}}_{\text{1}}})\text{/RT}\mathrm{....}\left(\text{iii}\right)$

${\text{Given\hspace{0.17em}E}}_{{\text{a}}_{\text{2}}}{\text{\hspace{0.17em}=\hspace{0.17em}2E}}_{{\text{a}}_{\text{1}}}$

On substituting this value in eqn. (iii)

${\text{k}}_{\text{1}}{\text{\hspace{0.17em}=\hspace{0.17em}k}}_{\text{2}}{\text{\hspace{0.17em}A\hspace{0.17em}×\hspace{0.17em}e}}^{{\text{E}}_{{\text{a}}_{\text{1}}}\text{/RT}}$