By combining the quark model and the atom-like structure of baryons described in the Scale-Symmetric Theory (SST) we have described the solar neutrino problem and generations of quarks. According to SST, there is a similarity of shapes and equality of mass ratios of the components of the three fundamental cores, i.e. of the core of lightest neutrinos, core of baryons, and the core of the Protoworld that was composed of dark matter. Within such a similarity we described the origin of the large mixing angle 33.089 degrees and the origin of the mass-squared splitting that define the solar neutrino oscillations. In our description, there appears imaginary mass and activation of the solar neutrino oscillations that can be damped. We showed that survival probability for the solar electron-neutrinos decreases from 1/2 at low energies of the electron-neutrinos (it is a mean value) to 1/3 for electron-neutrino energy equal to or higher than 9.345 MeV. We also described the atmospheric neutrino oscillations. SST leads to a minimum in the curve describing the dependence of the survival probability on neutrino energy for the atmospheric muon-like neutrinos for ∼500 km/GeV — it is consistent with experimental data. From SST follows that there are three generations of leptons and four generations of quarks and that the eight quarks combine into four pairs, i.e. d and u, s and c, b and t, and b’ ≈ 2.68 TeV and t’ ≈ 14.76 TeV. We described also the dark-matter (DM) field.