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In the wake of the recent measurements of the decays $B_c\to J/\psi\,\pi(K)$and $B_c\to J/\psi\,\ell\nu_\ell$ reported by the LHCb Collaboration wecalculate the form factors for the $B_c\to J/\psi$ and $B_c\to \eta_{c}$transitions in full kinematical region within covariant confined quark model.Then we use the calculated form factors to evaluate the partial decay widths ofthe above-mentioned semileptonic and nonleptonic decays of the $B_{c}$ meson.We find that the theoretical predictions on the ratios of $\mathcal{R}_{K^{+}/\pi^{+}}$ and $\mathcal{R_{\pi^{+}/ \mu^{+} \nu}}$ are in good agreement withlast LHCb-data. However, the prediction for the $\mathcal{R}_{J/\psi}$ is foundto be underestimated.

The decays $B_{c}\to J/\psi+\bar\ell\nu_\ell$ and $B_{c}\to J/\psi + \pi(K)$ in covariant confined quark model