The redox changes are as follows:
Fe⟶Fe2++2e
Fe2+⟶Fe3++e
5e+Mn7+⟶Mn2+
∴ Meq. of Fe2+ = Meq. of KMnO4
w(561)×=47.2×0.112
∴wFe2+=0.296g
∴ Purity of Fe=0.296×1000.804=36.82%
Now, Fe3O4⟶3Fe
∵3×56gFe obtained by 232gFe3O4
∴0.296gFe is obtained by 232×0.29656×3=0.409gFe3O4
∴% of Fe3O4=0.4090.804×100=50.84%
So, nearest integer value is 51.