  The bremsstrahlung flux-averaged cross-sections $\langle{\sigma(E_{\rm{\gamma
max}})}\rangle$ and the cross-sections per equivalent photon
$\langle{\sigma(E_{\rm{\gamma max}})_{\rm{Q}}}\rangle$ were measured for the
photonuclear multiparticle reaction $^{27}\!\rm{Al}(\gamma,\textit{x};
\textit{x} = {^{3}\rm{He}} + pd + 2pn)^{24}\rm{Na}$ at bremsstrahlung end-point
energies ranging from 40 MeV to 95 MeV. The experiments were performed using
the beam from the NSC KIPT electron linear accelerator LUE-40 with the use of
the $\gamma$-activation technique. The bremsstrahlung quantum flux was
calculated with the program GEANT4 and, in addition, was monitored by means of
the $^{100}\rm{Mo}(\gamma,n)^{99}\rm{Mo}$ reaction. The cross-sections
$\sigma(E)$ were computed using the TALYS1.9 code with the default options. The
measured average cross-sections $\langle{\sigma(E_{\rm{\gamma max}})}\rangle$
and $\langle{\sigma(E_{\rm{\gamma max}})_{\rm{Q}}}\rangle$ have appeared to be
higher by factors of 2.0 to 2.4 than the theoretical results. The experimental
results have been found to be in good agreement with the data of other
laboratories. Consideration is given to special features of calculation of
$\langle{\sigma(E_{\rm{\gamma max}})}\rangle$ and $\langle{\sigma(E_{\rm{\gamma
max}})_{\rm{Q}}}\rangle$ for the
$^{27}\!\rm{Al}(\gamma,\textit{x})^{24}\rm{Na}$ reaction, with occurrence of
three $^{27}\!\rm{Al}$ photodisintegration channels. The paper also discusses
the possibility of using the $^{27}\!\rm{Al}(\gamma,\textit{x})^{24}\rm{Na}$
reaction for monitoring the bremsstrahlung $\gamma$-quantum flux in the photon
energy region above 30 MeV.
