Abhay and Chintan start riding their motorcycles from the same point. Abhay rides 7 km north and then turns left and rides 4 km. Chintan rides 6 km west, then turns north and rides 7 km, and finally turns left and rides 8 km. Where is Abhay with respect to Chintan?

Introduction / Context:
This question tests two dimensional movement and relative position using directions on a plane. It is essentially a coordinate geometry or vector movement problem disguised as a word puzzle. By choosing a convenient reference frame and tracking each rider's displacement, we can determine their final coordinates and hence the relative position of one with respect to the other. Such problems are common in reasoning sections related to directions and movement.

Given Data / Assumptions:

Both riders start from the same point, taken as the origin (0, 0).
Positive x-axis represents east and positive y-axis represents north.
Abhay rides 7 km north, then 4 km west (since turning left from north points west).
Chintan rides 6 km west, then 7 km north, then 8 km west (left turn from north is also west).
We assume straight line segments for all movements.

Concept / Approach:
We treat each movement as a vector displacement and add them component wise. Each north or south movement changes the y coordinate, while each east or west movement changes the x coordinate. After obtaining the final coordinates of both Abhay and Chintan relative to the origin, we subtract the coordinates to find the position of Abhay relative to Chintan. The sign and magnitude of the difference in x coordinates directly give the east or west offset between them.

Step-by-Step Solution:
Step 1: Track Abhay's position. Start at (0, 0). Move 7 km north: new position = (0, 7). Turn left from north (towards west) and move 4 km: new position = (-4, 7). So Abhay ends at (-4, 7). Step 2: Track Chintan's position. Start at (0, 0). Move 6 km west: new position = (-6, 0). Turn north and move 7 km: new position = (-6, 7). Turn left from north (towards west) and move 8 km: new position = (-14, 7). So Chintan ends at (-14, 7). Step 3: Find Abhay's position relative to Chintan. Abhay = (-4, 7), Chintan = (-14, 7). Difference in x coordinates = -4 - ( -14 ) = 10. Same y coordinate means they are horizontally aligned. A positive difference in x from Chintan to Abhay means Abhay is 10 km east of Chintan.

Verification / Alternative check:
Visualising a simple grid helps. From the origin, Chintan ends 14 units left (west) and 7 units up (north). Abhay ends 4 units left and 7 units up. That is, Abhay is 10 units to the right (east) of Chintan, while both share the same vertical level. This picture matches the coordinate calculation exactly and confirms the result.

Why Other Options Are Wrong:
Option a (4 km East) incorrectly uses the difference between 6 and 4, ignoring the additional 8 km Chintan travels west in the last leg. Option b (10 km West) and option c (4 km Wes) both place Abhay on the wrong side of Chintan. The coordinates clearly show Abhay is east, not west, of Chintan by 10 km, so only 10 km East is correct.

Common Pitfalls:
Many students lose track of left and right turns, especially when the current direction is not east. Another common mistake is to add distances without considering direction signs, effectively ignoring positive and negative coordinates. Using a simple sketch or writing coordinates after each move can greatly reduce errors and makes the final relative position much easier to determine.

Final Answer:
Abhay is 10 km East of Chintan.