A binary star consists of two stars A (mass= 22 M s ) and B (mass= 11 M s ), where M s is the mass of the…

$\frac{{\text{L}}_{\text{Total}}}{{\text{L}}_{\text{B}}}=\frac{\left({\text{I}}_{\text{A}}+{\text{I}}_{\text{B}}\right)\omega }{{\text{I}}_{\text{B}}·\omega }$

(as $\omega$ will be same in both cases)
$\frac{{\text{L}}_{\text{Total}}}{{\text{L}}_{\text{B}}}=\frac{{\text{I}}_{\text{A}}}{{\text{I}}_{\text{B}}}+1=\frac{{\text{m}}_{\text{A}}{\text{r}}_{\text{A}}^2}{{\text{m}}_{\text{B}}{\text{r}}_{\text{B}}^2}+1$

$\left({\text{as m}}_{\text{A}}{\text{r}}_{\text{A}}={\text{m}}_{\text{B}}{\text{r}}_{\text{B}}\right)$

$\frac{{\text{L}}_{\text{Total}}}{{\text{L}}_{\text{B}}}=\frac{{\mathrm{m}}_{\mathrm{B}}}{{\mathrm{m}}_{\text{A}}}+1=0.5+1=1.5$