The magnetic structures of Fe₃BO₅ and Co₃BO₅ ludwigites have been studied experimentally by magnetic measurements and theoretically by the combination of the group theoretical analysis and semi empiric calculations of the superexchange interactions. The different collinear spin configurations in the triads 3-1-3 and 4-2-4 including ferromagnetic, antiferromagnetic and dimer have been considered. For Fe₃BO₅ the antiferromagnetic state with zero magnetic moment per unit cell, showing the lowest energy, results to be the most probable magnetic ground state. The unusual magnetic structure comprising two virtually independent orthogonal subsystems is formed to avoid heavy frustrations of superexchange interactions between the 3-1-3 and 4-2-4 spin ladders. In Co₃BO₅ the magnetic frustrations present for the Co³⁺ high-spin state are quenched for a Co³⁺ low spin state resulting in the ferrimagnetic long-range order. The obtained results are discussed in comparison with experimental magnetic data.