Balance the following equation: 

$$\begin{gathered} {\mathrm{FeC}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{4}} +{\mathrm{KMnO}}_{\mathrm{4}} + {\mathrm{H}}_{\mathrm{2}}{\mathrm{SO}}_{\mathrm{4}}\to \\ {\mathrm{Fe}}_{\mathrm{2}}{({\mathrm{SO}}_{\mathrm{4}}\mathrm{)}}_{\mathrm{2}} +{\mathrm{CO}}_{\mathrm{2}} +{\mathrm{MnSO}}_{\mathrm{4}} + {\mathrm{K}}_{\mathrm{2}}{\mathrm{SO}}_{\mathrm{4}} + {\mathrm{H}}_{\mathrm{2}}\mathrm{O} \end{gathered}$$ 

A balanced chemical reaction involves the same number of elements on both sides of the reaction. Consider the options;
In option A; the number of atoms on both sides are equal as follows:
Fe-10
C-20
O-196
K-6
Mn-6
H-48
S-24
Therefore balanced chemical reaction is

${\text{10FeC}}_{\text{2}}{\text{O}}_{\text{4}}{\text{ + 6KMnO}}_{\text{4}}{\text{ + 24H}}_{\text{2}}{\text{SO}}_{\text{4}}\to {\text{5Fe}}_{\text{2}}{\text{(SO}}_{\text{4}}{\text{)}}_{\text{2}}{\text{ + 20CO}}_{\text{2}}{\text{ + 6MnSO}}_{\text{4}}{\text{ + 3K}}_{\text{2}}{\text{SO}}_{\text{4}}{\text{ + 24H}}_{\text{2}}\text{O}$