The distance between two stars of masses 3 M _ S and 6 M _ S is 9R...

$T = \dfrac{2\pi{R}^{3 / 2}}{\sqrt{G{M}_{S}}}$

For binary stars,

$T ' = \dfrac{2\pi{r}^{3 / 2}}{\sqrt{G\left({M}_{1} + {M}_{2}\right)}}$

Put ${M}_{1} = 3{M}_{S}$,${M}_{2} = 6{M}_{S}$ and $r = 9R$

$T ' = \dfrac{2\pi \times {9}^{3 / 2} \times {R}^{3 / 2}}{\sqrt{G\left(3{M}_{S} + 6{M}_{S}\right)}} = \dfrac{2\pi \times {9}^{3 / 2} \times {R}^{3 / 2}}{{9}^{1 / 2}\sqrt{G{M}_{S}}} = 9\left(\dfrac{2\pi{R}^{3 / 2}}{\sqrt{G{M}_{S}}}\right)$

$∴ T ' = 9T$

Value of $n = 9$.