A man walks 3 km towards the west, then turns towards the south and walks 7 km, then turns towards the east and walks 3 km, and finally turns to his right and walks 5 km. Where is he now with respect to his original starting position?

Introduction / Context:
This is a classic direction sense problem in which a person walks in several straight line segments, changing direction at right angles. The objective is to track the path and determine the final position in terms of both distance and direction from the starting point. Questions of this type train spatial reasoning skills and are widely used in competitive examinations to test basic logical and geometric understanding without requiring any advanced mathematics.

Given Data / Assumptions:

• The man starts from a fixed starting point.
• He first walks 3 km towards the west.
• He then turns towards the south and walks 7 km.
• After that he turns towards the east and walks 3 km.
• Finally he turns to his right and walks 5 km.
• All turns are right angle turns and the ground is assumed to be flat and level.

Concept / Approach:
We use a simple coordinate geometry idea. Take the starting point as (0, 0). West movement means decreasing the x coordinate, east movement means increasing it. North means increasing the y coordinate and south means decreasing it. When the man turns, we carefully note his new facing direction before handling the next segment. At the end, the difference between the final coordinates and the origin gives the net displacement, which we then convert back into plain language as distance and direction from the starting point.

Step-by-Step Solution:
Step 1: Start from the origin, represented as (0, 0).Step 2: The man walks 3 km west, so the x coordinate decreases by 3 and the new position is (-3, 0).Step 3: He now faces west. Turning towards the south means he faces downward on our diagram. Walking 7 km south decreases the y coordinate, so the position becomes (-3, -7).Step 4: From this point he turns towards the east. Moving 3 km east increases the x coordinate by 3, giving a new position of (0, -7).Step 5: At (0, -7), he is facing east. A right turn from east means he now faces south again. Walking 5 km south decreases the y coordinate by another 5, leading to a final position of (0, -12).Step 6: Comparing with the starting point (0, 0), his x coordinate is unchanged and the y coordinate is -12. Therefore he is 12 km to the south of his starting point.

Verification / Alternative check:
Instead of coordinates, we can summarise the vertical and horizontal movements. Horizontally, he first walks 3 km west and later 3 km east, so these cancel each other and he has no net east west displacement. Vertically, he walks a total of 7 km south first and later another 5 km south, making a total of 12 km south. Since there is no northward movement, the overall displacement is directly 12 km south from the origin. This cross check matches the coordinate method and confirms the result.

Why Other Options Are Wrong:
Option A (12 km North) reverses the correct direction, confusing south with north. Option B (2 km South) incorrectly subtracts some distances and does not follow the complete path. Option D (2 km North) is inconsistent because there is no northward movement in any step. Only option C correctly captures both the magnitude and the direction: 12 km away from the starting point towards the south.

Common Pitfalls:
Many candidates forget to adjust the concept of left and right according to the current facing direction of the walker. Another common mistake is to add all distances in a straight manner and ignore cancellation. Using a rough sketch or simple coordinate representation helps to avoid these errors. Always account for each turn and remember that movements in opposite directions can cancel out when considering net displacement.

Final Answer:
The man is finally located 12 km to the south of his starting point, so the correct option is “12 km South”.