The dipole moment of $\mathrm{HX}$ is $1.2\mathrm{D}$. If the % ionic character of the bond is 25 %, then it's bond length is

$$\begin{gathered} {\mathrm{\mu }}_{\mathrm{obs}}=1.2\mathrm{D}= 1.2\times {10}^{-18}\mathrm{esu}.\mathrm{cm} \\ \mathrm{q}=4.8\times {10}^{-10}\mathrm{esu} \end{gathered}$$

% ionic character (I.C.)$=\frac{{\mathrm{\mu }}_{\mathrm{obs}}}{{\mathrm{\mu }}_{\mathrm{cal}}}\times 100$

$$\begin{gathered} {\mathrm{\mu }}_{\mathrm{cal}}=\mathrm{q}\times \mathrm{d} \\ \mathrm{d}=\frac{{\mathrm{\mu }}_{\mathrm{obs}}}{\mathrm{q}\times \%\mathrm{I}.\mathrm{C}.}\times 100 \\ \mathrm{d}=\frac{1.2\times {10}^{-18}\mathrm{esu}.\mathrm{cm}}{4.8\times {10}^{-10}\mathrm{esu}\times 25}\times 100 \\ \mathrm{d}={10}^{-8}\mathrm{cm}={10}^{-10}\mathrm{m} \end{gathered}$$

Hence, correct answer is option B, ${10}^{-10}\mathrm{m}$