\(\overset{+7}{KMnO_4 }+ \overset{+2}{Fe}SO_4+ H_2SO_4 \longrightarrow K_2SO_4 + \overset{+2}{Mn}SO_4 + \overset{+2}{Fe_2}(SO_4)_3 + H_2O\)
Increase in O.N. per FeSO4 (from +2 to +3) = 1
Since one Fe2(SO4)3 can only be derived from 2FeSO4
\(\therefore\) Total increase in O.N. = 2
Decrease in O.N. per KMnO4 (from +7 to +2) = 5
Hence multiply FeSO4 by 5 and KMnO4 by 2 so as to make total increase and decrease in O.N. the same
\(\therefore\) 2KMnO4 + 10FeSO4 + 8H2SO4 → K2SO4 + 2MnSO4 + 5Fe2(SO4)3 + H2O