The relative production rate of $B^{0}_{s}$ and $B^{0}$ mesons is determined with the hadronic decays $B^{0}_{s} rightarrow D^{-}_{s}pi^{+}$ and $B^0 rightarrow D^{-}K^{+}$. The measurement uses data corresponding to 1.0 fb$^{-1}$ of $pp$ collisions at a centre-of-mass energy of $sqrt{s}=7$ TeV recorded in the forward region with the LHCb experiment. The ratio of production rates, $f_{s}/f_{d}$, is measured to be $0.238 pm 0.004 pm 0.015 pm 0.021 $, where the first uncertainty is statistical, the second systematic, and the third theoretical. This is combined with a previous LHCb measurement to obtain $f_{s}/f_{d} = 0.256 pm 0.020$. The dependence of $f_{s}/f_{d}$ on the transverse momentum and pseudorapidity of the $B$ meson is determined using the decays $B^{0}_{s} rightarrow D^{-}_{s}pi^{+}$ and $B^{0} rightarrow D^{-}pi^{+}$. There is evidence for a decrease with increasing transverse momentum, whereas the ratio remains constant as a function of pseudorapidity. In addition, the ratio of branching fractions of the decays $B^{0} rightarrow D^{-}K^{+}$ and $B^{0} rightarrow D^{-}pi^{+}$ is measured to be $0.0822 pm 0.0011 (textrm{stat}) pm 0.0025 (textrm{syst})$.
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