Krishna walks for 10km towards the North. From here, he walks back 6km towards the South. Then he walks 3km towards the East. How far and in which direction is he with reference to his starting point?

It is given that Krishna walks 10km North and then 6km back south, so effectively, he has walked 4 km North. 
It is then given that he walks 3km East. 

North and East are directions that are at right angles to each other. We know he has walked 4km North and 3km East, 
To find the distance to his starting point, we use the Pythagoras theorem to find the effective distance 
$$\sqrt{3^2+4^2}=5$$

Hence, the answer is 5km North-East.