Punit starts from point R and walks straight 10 km towards the west, then turns right and walks 12 km, and again turns right and walks straight 7 km. In which direction is Punit now located with respect to point R?

Introduction / Context:
This direction sense question requires determining the final direction of a person from his starting point after a few straight movements and right angle turns. Punit starts at point R, walks west, then turns right twice and walks given distances. We are asked for his direction from point R, not the exact distance. This involves combining horizontal and vertical displacements to see which quadrant his final position occupies.

Given Data / Assumptions:

• Punit starts at point R.
• He walks 10 km west from R.
• He turns right and walks 12 km.
• He turns right again and walks 7 km.
• All turns are right angle turns, with no diagonal movement.
• We interpret right turns as clockwise 90 degree rotations from the current facing direction.

Concept / Approach:
We can track Punit's path using coordinates. By setting point R at the origin and marking western movement as negative x and northern movement as positive y, each leg of his path can be recorded as a change in coordinates. Right turns are interpreted based on the direction he is facing at that moment. Once we know his final coordinates, we can infer whether he lies to the north, south, east, or west of R, and thus identify the final direction such as north west or south east.

Step-by-Step Solution:
Step 1: Place point R at (0, 0).Step 2: Punit walks 10 km west, so his new position is (−10, 0), and he is facing west.Step 3: A right turn from west means he now faces north. Walking 12 km north takes him to (−10, 12).Step 4: Another right turn from north means he now faces east. Walking 7 km east takes him to (−3, 12).Step 5: His final coordinates relative to R are (−3, 12). This means he is 3 km west and 12 km north of point R.Step 6: Being both west and north of R places him in the north west direction relative to R.

Verification / Alternative check:
A sketch of the path confirms this conclusion. From R, draw a horizontal segment 10 km to the left to represent the first leg. Then draw a vertical segment 12 km upward to show the second leg. Finally, draw a horizontal segment 7 km to the right for the third leg. The end point clearly lies above and slightly to the left of R. This visual inspection confirms that Punit is north west of R and not in any other quadrant.

Why Other Options Are Wrong:
North east would require him to be east of R as well as north, which contradicts the fact that his x coordinate is negative. South east and south west would place him below R in the diagram, but his y coordinate is positive, indicating a position north of R. Pure east would require the x coordinate to be positive and y to be zero, which is not the case. Only the north west direction fits the sign pattern of his final coordinates.

Common Pitfalls:
Some candidates mistakenly treat both right turns as turning towards the south after the first leg, which changes the orientation of the path entirely. Others forget that a right turn from west leads to north, not south. It is very helpful to draw the four directions and indicate facing direction at each stage to avoid such misinterpretations. Keeping track of coordinates instead of relying only on verbal descriptions makes the reasoning much more solid.

Final Answer:
From point R, Punit's final position lies in the North-West direction.