A cyclist runs 6 km due east and then turns left. After running 5 km, he again turns left and runs 4 km. Then he turns right and moves 3 km. Then he again turns left and runs 8 km at a stretch. How far is he now from his original place?

As per the given information,

A cyclist runs 6 km due east and then turns left. After running 5 km, he again turns left and runs 4 km. Then he turns right and moves 3 km. Then he again turns left and runs 8 km at a stretch.

So, the following diagram can be drawn:

Now,

Distance between AF is calculated by using Pythagoras theorem:

→ (AF)2 = (AG)2 + (GF)2 

→ (AF)2 = (8)2 + (6)2 

→ (AF)2 = 64 + 36

→ (AF)2 = 100

→ AF= 10 km

Clearly, the cyclist is '10 km' far away from his original place.

Hence, the correct answer is "10 km".