10 people: Naman, Rishabh, Amisha, Nidhi, Ruchi, Rishi, Ankita, Kanak, Ruchika, and Ayushi.
In Row 1: Ankita, Nidhi, Naman, Kanak, and Ruchika (Facing South)
In Row 2: Rishi, Ruchi, Amisha, Rishabh, Ayushi (Facing North)
1. Naman is sitting third to the right of Ruchika. Ruchika faces Rishi, on combining these two sentences we get 2 possible cases for the position of Naman and Ruchika.
Case 1: When Ruchika sits second from the left end of the row.

Case 2: When Ruchika sits on the extreme end from the left end of the row.

2. Nidhi sits opposite to the person who sits second to the right of Ruchi. Neither Amisha nor Nidhi sit on the extreme ends of the row.
Case 1: When Ruchi sits at the extreme end of the row from the left end.

Case 2: When Ruchi sits at the extreme end of the row from the left end.

Case 2a: When Ruchi sits second from the left end of the row.

3. Amisha sits second to the left of Rishi, and also Ayushi is the immediate left of Rishi.



4. Ankita is not an immediate neighbor of Naman, and does not face Ayushi, from this line our Case 2 and Case 2a gets eliminated, as no other place for Ankita is left to sit in these cases except to the positions on the immediate left or right of Naman.
So, Ankita will sit on the extreme end of the row from the right end facing Rishabh.
Now, only one place is left for the position of Kanak which is to the immediate left of Naman.

The final arrangement:

Let's check each option:
Rishabh: Sits at the extreme end.
Ankita: Sit at the extreme end.
Ruchi: Sit at the extreme end.
Naman: Sit at the extreme end.
Ruchika: Sit at the second left position from the left end.
Ruchika does not belong to that group.