Arun and Amit start walking from two different points A and B respectively. Arun walks 2 km towards the north, then 3 km towards the east, again 4 km towards the north and finally 5 km towards the east to reach point C. Similarly, Amit starts from B, walks 2 km towards the north, then 3 km towards the west and finally 4 km towards the north to meet Arun at the same point C. What is the straight line distance between the starting points A and B?

Introduction / Context:
This question involves two people starting from different points and walking along different paths to meet at a common point. The topic belongs to direction sense and basic coordinate geometry in verbal reasoning. The main goal is to reconstruct their paths in a simple coordinate system and calculate the distance between their original starting points. It tests the ability to convert word descriptions into a clear diagram or set of coordinates.

Given Data / Assumptions:

• Arun starts from point A.
• Arun walks 2 km north, 3 km east, 4 km north, and 5 km east to reach point C.
• Amit starts from point B.
• Amit walks 2 km north, 3 km west, and 4 km north to reach the same point C.
• All directions are along standard north south and east west axes, and there is no diagonal movement.

Concept / Approach:
We can treat the paths as movements on a grid. By placing point A at the origin of a coordinate system, we can find the coordinates of point C using Arun's path. Then we use Amit's path in reverse to determine where point B must be located so that Amit also ends at C. Once we have coordinates for both A and B, the distance between them can be determined by simple horizontal separation, because they lie on the same east west line in this setup.

Step-by-Step Solution:
Step 1: Place point A at (0, 0) in a coordinate plane with east as positive x and north as positive y.Step 2: Track Arun's movement. After 2 km north he is at (0, 2). After 3 km east he is at (3, 2). After another 4 km north he is at (3, 6). After 5 km east he reaches point C at (8, 6).Step 3: Let Amit start at point B with coordinates (x, y). After 2 km north he is at (x, y + 2). After 3 km west he is at (x − 3, y + 2). After 4 km north he reaches C at (x − 3, y + 6).Step 4: Since both reach the same point C, we equate the coordinates: x − 3 = 8 and y + 6 = 6.Step 5: Solving, we get x = 11 and y = 0, so B is at (11, 0), while A is at (0, 0).Step 6: The distance between A and B is simply the horizontal separation, which is 11 km.

Verification / Alternative check:
We can verify by running Amit's path explicitly from (11, 0). After 2 km north he reaches (11, 2). After 3 km west he reaches (8, 2). After 4 km north he reaches (8, 6), which matches the coordinate of point C obtained from Arun's path. Because both meet at the same coordinate and the separation between A and B is a straight horizontal segment of length 11, the answer is confirmed as 11 km.

Why Other Options Are Wrong:
The option 5 km is far too small compared to the size of the grid and does not match any calculated separation. The options 8 km and 7 km might be guessed from partial movements but do not satisfy the coordinate equations. The option 13 km is a common Pythagorean triple value, but here the separation is purely horizontal with no vertical difference, so 13 km is not appropriate. Only 11 km matches the derived coordinates of the two starting points.

Common Pitfalls:
One common error is to ignore the fact that Arun and Amit meet at the same point and instead treat their paths independently, making it hard to set up correct equations. Another mistake is mixing up east and west movements when writing coordinates, which reverses signs and leads to wrong distances. Drawing a rough diagram or setting up a coordinate table avoids confusion and makes the logic of the problem much clearer.

Final Answer:
The distance between Arun's starting point A and Amit's starting point B is a straight line segment of length 11 km along the east west direction.