Total number of persons in the group is 65 out of which 48 persons like ski-diving and 27 like car driving.

Let the number of persons who like both ski-diving and car driving be ' $\(x\)$ ', so the number of persons who like only ski-diving and those who like only car driving would be ( $\(48-x\)$ ) & \( (27 -x)\)$ respectively.

Now, filling this information in the two set Venn diagram, we get

We know $\((48-x)+x+(27-x)=65 \Rightarrow x=10\)$

Hence the number of persons who like only Sky-diving $(48-x)=(48-10)=38$, so the answer is $\((C)\)$.