Measurements are presented of the branching fractions of the decays B S 0 → D S ∓ K ∓ and B 0 → D S − K + relative to the decays B S 0 → D S − π + and B 0 → D − π +, respectively. The data used correspond to an integrated luminosity of 3.0 fb−1 of proton-proton collisions. The ratios of branching fractions are $$ \frac{\mathrm{\mathcal{B}}\left({B}_{\mathrm{s}}^0\to {D}_{\mathrm{s}}^{\mp }{K}^{\mp}\right)}{\mathrm{\mathcal{B}}\left({B}_{\mathrm{s}}^0\to {D}_{\mathrm{s}}^{-}{\pi}^{+}\right)}=0.0752\pm 0.0015\pm 0.0019 $$ and $$ \frac{\mathrm{\mathcal{B}}\left({B}^0\to {D}_{\mathrm{s}}^{-}{K}^{+}\right)}{\mathrm{\mathcal{B}}\left({B}^0\to {D}^{-}{\pi}^{+}\right)}=0.0129\pm 0.0005\pm 0.0008, $$ where the uncertainties are statistical and systematic, respectively.