The bond order of ${\mathrm{O}}_2^{+}$ is x. The bond orders of ${\mathrm{O}}_2^{-}$and ${\mathrm{O}}_2^{2+}$ are respectively

Bond order for ${\mathrm{O}}_2^{+}$ is:

$\frac{10-5}{2}=\frac{5}{2}=2.5=\mathrm{X}$

Bond order for ${\mathrm{O}}_2^{-}$ is:

$\frac{10-7}{2}=\frac{3}{2}=1.5$

Bond order for ${\mathrm{O}}_2^{2+}$ is:

$\frac{10-4}{2}=\frac{6}{2}=3$

$$\begin{gathered} 2.5\times \frac{3}{5}=1.5 (\mathrm{bond} \mathrm{order} \mathrm{of} {\mathrm{O}}_2^{-}) \\ \mathrm{x}\times \frac{3}{5}=1.5 \\ 2.5\times \frac{6}{5}=3 (\mathrm{bond} \mathrm{order} \mathrm{of} {\mathrm{O}}_2^{2+}) \\ \mathrm{x}\times \frac{6}{5}=3 \end{gathered}$$