Find oxidation number of K in $K_2O$

Let oxidation number of potassium be $x$.

Oxygen in normal oxide is $-2$.

So, $2x + (-2) = 0$ $2x = 2$ $x = +1$

Find oxidation number of K in $K_2O_2$

This is a peroxide. In peroxide, each oxygen has oxidation number $-1$.

Let oxidation number of potassium be $x$.

$2x + 2(-1) = 0$ $2x - 2 = 0$ $2x = 2$ $x = +1$

Find oxidation number of K in $KO_2$

This is a superoxide. In superoxide ion $O_2^-$, the total oxidation number of two oxygens is $-1$, so average oxidation number of each oxygen is $-\frac{1}{2}$.

Let oxidation number of potassium be $x$.

$x + \,(-1) = 0$ $x = +1$

Hence potassium has oxidation number $+1$ here also.

Compare with options

The oxidation numbers of potassium in $K_2O$, $K_2O_2$, and $KO_2$ are: $+1,\ +1,\ +1$

Therefore, the correct option is B.