The ratio of the production cross sections times branching fractions (sigma(B-c(+/-))B(B-c(+/-) -> J/psi pi(+/-)))/(sigma(B-+/-)B(B-+/- -> J/psi K-+/-)) is studied in proton-proton collisions at a center-of-mass energy of 7TeV with the CMS detector at the LHC. The kinematic region investigated requires B-c(+/-) and B-+/- mesons with transverse momentum p(T) > 15 GeV and rapidity vertical bar y vertical bar < 1.6. The data sample corresponds to an integrated luminosity of 5.1 fb(-1). The ratio is determined to be [0.48 +/- 0.05 (stat) +/- 0.03 (syst) +/- 0.05 (tau(Bc))]%. The B-c(+/-) -> J/psi pi(+/-)pi(+/-)pi(-/+) decay is also observed in the same data sample. Using a model-independent method developed to measure the efficiency given the presence of resonant behaviour in the three-pion system, the ratio of the branching fractions B-c(+/-) -> J/psi pi(+/-)pi(+/-)pi(-/+)/B(B-c(+/-) -> J/psi pi(+/-)) is measured to be 2.55 +/- 0.80 (stat) +/- 0.33 (syst)(-0.01)(+0.04) (tau(Bc)), consistent with the previous LHCb result.