Balance the following equations by oxidation number method.
$C O + F e_{3} O_{4} \to F e O + C O_{2}$

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Solution

$C O F e_{3} O_{4} \to F e O + C O_{2}$
$C O \to C O_{2}$ oxidation by $2$ units
$F e_{3} O_{4} \to F e O$ reduction by $2 / 3$ units
Therefore,
$2 / 3 C O \to 2 / 3 C O_{2}$
or, $2 C O \to 2 / 3 C O_{2}$
and, $2 F e_{3} O_{4} \to 2 F e O$
Balancing $F e, 2 F e_{3} O_{4} \to 6 F e O$
Equation 1 + Equation 2:
$2 C O + 2 F e_{3} O_{4} \to 6 F e O + 2 C O_{2}$ divided by $2$
$C O + F e_{3} O_{4} \to 3 F e O + C O_{2}$

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