In a $S_{N}2$ substitution reaction of the type 

$\mathrm{R}-\mathrm{Br}+{\mathrm{Cl}}^{-}\stackrel{DMF}{\to }\mathrm{R}-\mathrm{Cl}+{\mathrm{Br}}^{-}$

Which one of the following has the highest relative rate?

$S_{N}2$ mechanism is followed in case of primary and secondary alkyl halides i.e $S_{N}2$ reaction is favoured by small groups on the carbon atoms attached the halogen so Primary is more reactive than secondary and tertiary alkyl halides