IGDTUW 2025 — Reasoning PYQ

To determine the final position with respect to the starting point, we can use the Pythagorean theorem by mapping his movements on a 2D coordinate plane, where the starting point is $(0,0)$.

1. Movement 1: He walks 10 km North.

   • New position: $(0,10)$

2. Movement 2: He walks 6 km South.

   • New position: $(0,10-6)=(0,4)$

3. Movement 3: He walks 3 km East.

   • New position: $(0+3,4)=(3,4)$

Now, we calculate the distance from the starting point $(0,0)$ to the final position $(3,4)$ using the distance formula:

$$Distance=\sqrt{x^2+y^2}$$

$$Distance=\sqrt{3^2+4^2}$$

$$Distance=\sqrt{9+16}$$

$$Distance=\sqrt{25}$$

$$Distance=5\text{ km}$$

Since he is at a position where both coordinates are positive ($x=3$ East, $y=4$ North), he is in the North-east direction relative to his starting point.

The correct answer is (b) 5 kilometers North-east.