Abhinav starts his journey and travels 10 kilometres towards the north. Then he turns left and travels 6 kilometres. Next, he turns right and covers another 7 kilometres. Finally, he turns right once more and travels 6 kilometres. How far, in kilometres, is Abhinav from the point at which he started his journey (measured in a straight line)?

Introduction / Context:
This problem is a direction sense and distance question combining several turns and segments of different lengths. Such questions can easily confuse learners if they only imagine the path mentally. The task is to find the straight line distance between Abhinav's starting point and his final position after moving north, then left, then right twice. The question checks spatial awareness and the ability to track movements using either a sketch or coordinate style reasoning.

Given Data / Assumptions:

• Abhinav first travels 10 kilometres towards the north.
• He then turns left and travels 6 kilometres.
• After that he turns right and covers 7 kilometres.
• Finally he turns right again and travels another 6 kilometres.
• All turns are at right angles (90 degrees).
• We must find the straight line distance from the starting point to the final point.

Concept / Approach:
The most systematic method is to use a coordinate system. Choose the starting point as the origin (0, 0). Take north as positive y, south as negative y, east as positive x and west as negative x. At each step, update the coordinates based on the current facing direction and the distance travelled. Once we know the final coordinates, we can find the displacement using Pythagoras: distance = square root of (x^2 + y^2). Since all turns here are at right angles, the final displacement often turns out to be a simple integer value.

Step-by-Step Solution:
Step 1: Assume Abhinav starts at (0, 0), initially facing north. Step 2: He walks 10 kilometres north, so his position becomes (0, 10). Step 3: From facing north, a left turn leads to west. Walking 6 kilometres west, he reaches (-6, 10). Step 4: From facing west, a right turn leads back to north. Travelling 7 kilometres north, he reaches (-6, 17). Step 5: From facing north again, another right turn leads to east. Walking 6 kilometres east, he moves from (-6, 17) to (0, 17). Step 6: His final coordinates are therefore (0, 17). This means he is directly north of the starting point with no east or west displacement. Step 7: The straight line distance between (0, 0) and (0, 17) is simply 17 kilometres.

Verification / Alternative check:
We can confirm this result by tracking net vertical and horizontal movement. Horizontally, Abhinav first moves 6 kilometres west and later 6 kilometres east, which cancel out completely, leaving zero horizontal displacement. Vertically, he moves 10 kilometres north and an additional 7 kilometres north, with no southward movement, so his total vertical displacement is 17 kilometres north. Since only one component is non zero, the displacement distance is simply 17 kilometres, matching the coordinate approach.

Why Other Options Are Wrong:

• Option A, 14 kilometres, may come from subtracting or incorrectly combining the vertical movements.
• Option B, 15 kilometres, and Option C, 16 kilometres, are typical distractors from mistaken Pythagoras applications or rough estimations.
• Option E, 13 kilometres, is another incorrect result that can arise from misreading the distances or mixing up left and right turns.

Common Pitfalls:
Common mistakes include confusing left and right when facing south or west, and failing to cancel out equal and opposite horizontal movements. Some students also attempt to add distances in different directions directly without using vector style reasoning. Drawing the path or maintaining a simple table of x and y coordinates at each step greatly reduces such errors and makes direction sense questions much easier to handle in timed exams.

Final Answer:
Abhinav is finally 17 kilometres away from his starting point, directly to the north, so the required distance is 17 kilometres.