It can be explained on the basis of E° values of Cr3+ | Cr2+ (–0.4 A)
Mn3+ | Mn2+(+ 1.5 V).
On the basis of these values, it is clear that Cr2+ has a greater tendency to oxidise into Cr3+, thus it acts as reducing agent.
Cr2+(aq) → Cr3+(aq) + e–
While Mn3+ has a greater tendency to reduce into Mn2+, thus it acts as oxidising agent.
Mn3+(aq) + e– → Mn2+(aq)