The structural, magnetic, and electronic properties of NdFe$_{0.5}$Mn$_{0.5}$O$_3$ have been studied in detail using bulk magnetization, neutron/x-ray diffraction and first principles density functional theory calculations. The material crystallizes in the orthorhombic $Pbnm$ structure, where both Mn and Fe occupy the same crystallographic site ($4b$). Mn/Fe sublattice of the compound orders in to a G-type antiferromagnetic phase close to 250,K where the magnetic structure belongs to ${Gamma}_{1}$ irreducible representation with spins aligned along the crystallographic $b$ direction. This is unconventional in the sense that most of the orthoferrites and orthochromites order in the ${Gamma}_{4}$ representation below the N{e}el temperature.This magnetic structure then undergoes a complete spin reorientation transition with temperature in the range 75,K$gtrsim$ T $gtrsim$ 25,K where the magnetic structure exists as a sum of two irreducible representations (${Gamma}_{1}$+${Gamma}_{2}$) as seen from neutron diffraction measurements. At 6,K, the magnetic structure belongs entirely to ${Gamma}_{2}$ representation with spins aligned antiferromagnetically along the crystallographic $c$ direction having a small ferromagnetic component ($F_x$). The unusual spin reorientation and correlation between magnetic ground state and electronic structure have been investigated using first principles calculations within GGA+U and GGA+U+SO formalisms.
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