As many as 10\% of OB-type stars have global magnetic fields, which is surprising given their internal structure is radiative near the surface. A direct probe of internal structure is pulsations, and some OB-type stars exhibit pressure modes ($\beta$ Cep pulsators) or gravity modes (slowly pulsating B-type stars; SPBs); a few rare cases of hybrid $\beta$ Cep/SPBs occupy a narrow instability strip in the H-R diagram... The most precise fundamental properties of stars are obtained from eclipsing binaries (EBs), and those in clusters with known ages and metallicities provide the most stringent constraints on theory. Here we report the discovery that HD 149834 in the $\sim$5 Myr cluster NGC 6193 is an EB comprising a hybrid $\beta$ Cep/SPB pulsator and a highly irradiated low-mass companion. We determine the masses, radii, and temperatures of both stars; the $\sim$9.7 M$_\odot$ primary resides in the instability strip where hybrid pulsations are theoretically predicted. The presence of both SPB and $\beta$ Cep pulsations indicates that the system has a near-solar metallicity, and is in the second half of the main-sequence lifetime. The radius of the $\sim$1.2 M$_\odot$ companion is consistent with theoretical pre-main-sequence isochrones at 5 Myr, but its temperature is much higher than expected, perhaps due to irradiation by the primary. The radius of the primary is larger than expected, unless its metallicity is super-solar. Finally, the light curve shows residual modulation consistent with the rotation of the primary, and Chandra observations reveal a flare, both of which suggest the presence of starspots and thus magnetism on the primary. (read more)