If mass of earth is $5.98\times 10^{24}$ kg and earth moon distance is $3.8\times 10^5$ km, the orbital period of moon, in days is

$M=5.98\times 10^{24}kg$

$R=3.8\times 10^{8}km$

The orbital time period of moon,

$T=2\pi \sqrt{\frac{R^3}{GM}}$

$T=2\times 3.14\sqrt{\frac{(3.8{)}^3\times 10^{24}}{6.67\times 10^{-11}\times 5.48\times 10^{24}}}$

$T=23.2427\times 10^{5}sec$

In days,

Time period, $T=\frac{23.2427\times 10^5}{60\times 60\times 24}day$

$T=27days$

The correct option is A.