A man walks 20 m towards the north, then turns to his right and walks 3 m, then turns left and walks 4 m, and from there walks another 4 m towards the east. How far is he from his initial position, and in which direction from the starting point is he now located?

Introduction / Context:
This problem is slightly different from simple direction sense questions because it asks for both distance and direction from the starting point after several turns and movements. To answer correctly, we must treat the displacements as sides of a right angled triangle and then apply the Pythagoras theorem to compute the straight line distance between the start and end positions. These questions develop a candidate's ability to combine geometry with direction sense reasoning.

Given Data / Assumptions:

• The man starts from an initial position.
• He walks 20 m towards the north.
• He then turns right and walks 3 m.
• Next, he turns left and walks 4 m.
• From that point, he walks 4 m towards the east.
• All paths are straight and all turns are right angle turns.

Concept / Approach:
We again use a coordinate system with the origin as the starting point. We convert every movement into a change in x or y coordinate. Once we find the final coordinates, we use the formula distance = square root of (x^2 + y^2) to calculate how far the man is from the origin. The direction is then inferred by observing the signs of the x and y coordinates, which tell us the quadrant in which the final point lies, such as north east.

Step-by-Step Solution:
Step 1: Start at (0, 0). The man first walks 20 m north to reach (0, 20).Step 2: From north, a right turn leads to facing east. Walking 3 m east changes the position to (3, 20).Step 3: He now faces east. A left turn from east makes him face north again. Walking 4 m north moves him to (3, 24).Step 4: From (3, 24), the problem says he walks 4 m towards the east, which leads to the final position (7, 24).Step 5: The net horizontal displacement from the origin is 7 m to the east (x = 7) and the net vertical displacement is 24 m to the north (y = 24).Step 6: The distance from the origin is given by the length of the hypotenuse of a right angled triangle: distance = square root of (7^2 + 24^2) = square root of (49 + 576) = square root of 625 = 25 m.Step 7: Since both x and y are positive, the man is in the north east direction from the starting point.

Verification / Alternative check:
We can quickly recognise the famous Pythagorean triple 7, 24, 25. The legs of the triangle are 7 m and 24 m and the hypotenuse is 25 m, which confirms the calculation. A mental diagram with the starting point, intermediate turns and final point also clearly shows that the end point lies diagonally to the north east of the origin, not directly north or east.

Why Other Options Are Wrong:
Option A (25 m East) has the correct distance but wrong direction, ignoring the significant 24 m northward component. Option C (20 m North) confuses the first leg of the journey with the total displacement. Option D (24 m North) uses the vertical component only and omits the horizontal component. Only option B correctly combines both distance and quadrant by stating 25 m in the north east direction from the starting point.

Common Pitfalls:
A common mistake is to add all distances numerically rather than treating them as perpendicular components. Another frequent error is to misinterpret right and left turns when the orientation changes multiple times. The safest method is to maintain a small coordinate system or diagram and to mark each movement in sequence, then apply Pythagoras theorem for the final displacement when both x and y components are non zero.

Final Answer:
The man is finally located 25 m away from his starting point in the north east direction, so the correct option is “25 m North-East”.