Karan travels 20 km towards the south, and then takes a left, and travels 35 km further. Again, he takes a left and travels 20 km further. How far is he from his original position?

Let's track Karan's movements step-by-step from his starting point (0,0):
Moves 20 km South → reached point (0,−20).

Takes a left turn (facing East) and travels 35 km → reached point (35,−20).

Takes another left turn (facing North) and travels 20 km → reached point (35,−20+20)=(35,0).

Now, his final position is (35,0) and his starting position was (0,0).
The distance between the original and final position is simply along the horizontal axis:

Distance=35 km