Sandeep walks 3 km east, turns left and walks 5 km, then turns left again and walks 8 km. How far and in which direction is he from his starting point?

Explanation

1. 01

   Left from east is north; left from north is west.

2. 02

   East–west: 3 km east, then 8 km west, leaving 5 km west.

3. 03

   North–south: 5 km north.

4. 04

   5 km west and 5 km north are equal, so he is exactly north-west of the start, at $\sqrt{5^2 + 5^2} = 5\sqrt{2}$ km.