A measurement of the ratio of the branching fractions of the View the MathML sourceBs0 meson to J/ψf0(980)J/ψf0(980) and to J/ψϕ(1020)J/ψϕ(1020) is presented. The J/ψJ/ψ, f0(980)f0(980), and ϕ(1020)ϕ(1020) are observed through their decays to μ+μ−μ+μ−, π+π−π+π−, and K+K−K+K−, respectively. The f0f0 and the ϕ are identified by requiring |Mπ+π−−974 MeV|<50 MeV|Mπ+π−−974 MeV|<50 MeV and |MK+K−−1020 MeV|<10 MeV|MK+K−−1020 MeV|<10 MeV. The analysis is based on a data sample of pp collisions at a centre-of-mass energy of 7 TeV, collected by the CMS experiment at the LHC, corresponding to an integrated luminosity of 5.3 fb−1. The measured ratio is View the MathML sourceB(Bs0→J/ψf0)B(f0→π+π−)B(Bs0→J/ψϕ)B(ϕ→K+K−)=0.140±0.008(stat)±0.023(syst), where the first uncertainty is statistical and the second is systematic.