  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 we
calculate 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 of
the 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 with
last LHCb-data. However, the prediction for the $\mathcal{R}_{J/\psi}$ is found
to be underestimated.
