A marathon route starts from a fixed point and first goes 21 km towards the North.\nFrom there, the route turns towards the West and continues for 7 km, then turns towards the North again and continues for another 10 km.\nFinally, there is a right turn and the route goes on for 7 km to reach the finishing point.\nWhere is the finishing point located with reference to the starting point?

Introduction / Context:
This question describes the path of a marathon route using several straight-line segments and directional turns. The objective is to determine the net displacement of the finishing point with respect to the starting point. Such direction sense problems test your ability to convert a series of movements into a simplified overall position, often by visualizing or sketching a diagram and combining distances along the North–South and East–West axes separately.

Given Data / Assumptions:

• The route begins at a starting point taken as the origin.
• First, the route goes 21 km towards the North.
• Next, it turns towards the West and continues for 7 km.
• After that, it turns again towards the North and continues for 10 km.
• Finally, there is a right turn and the route continues for 7 km until the finishing point.
• Right turn from North means turning to the East, assuming standard compass conventions.
• All distances are measured in straight lines and each turn is a 90 degree turn.

Concept / Approach:
We can treat this situation as movement on a coordinate grid. The North–South movements affect the vertical coordinate, while the East–West movements affect the horizontal coordinate. If a segment goes West and a later segment goes East by the same amount, these displacements can cancel each other. The net position is then found by summing all North movements and subtracting South movements, and similarly for East and West if needed. In this specific question, you will see that the West and East movements cancel out, leaving only a vertical displacement relative to the starting point.

Step-by-Step Solution:
Step 1: Assume the starting point is at (0, 0). Step 2: The first movement is 21 km North, so the route reaches point A at (0, 21). Step 3: From A, the route turns West and goes 7 km, reaching point B at (-7, 21). Step 4: From B, the route turns North and travels 10 km, reaching point C at (-7, 31). Step 5: From C, there is a right turn. From facing North, a right turn means facing East. The route then goes 7 km East to reach the finishing point D at (0, 31). Step 6: Compare the coordinates of the starting point (0, 0) and finishing point (0, 31). There is no net East–West displacement (0 on both), but the finishing point is 31 km to the North of the starting point.

Verification / Alternative check:
Instead of plotting coordinates, we can track only the North–South and East–West components. Total Northward distance = 21 km + 10 km = 31 km. There is no Southward movement. Total Westward distance is 7 km, and later total Eastward distance is also 7 km, so these cancel each other. Therefore, the overall displacement is 31 km North from the start. This simple addition and cancellation method confirms the coordinate-based result and shows that the finishing point is exactly 31 km North of the starting position.

Why Other Options Are Wrong:
31 km South is wrong because the net vertical displacement is towards the North, not the South. 11 km North is incorrect because it ignores some of the Northward movement; it would arise only if 10 km of North movement were mistakenly subtracted. 11 km South is doubly incorrect, both in direction and in magnitude. 21 km North corresponds only to the first segment and does not account for the additional 10 km North travelled later in the route.

Common Pitfalls:
Students sometimes forget to include all Northward movements or fail to cancel out equal Eastward and Westward segments, leading to wrong net displacements. Another frequent error is mixing up left and right turns and therefore assigning the wrong direction to later segments. A quick sketch on paper with arrows and axes, or a small table tracking cumulative North–South and East–West distances, can greatly reduce such mistakes and make the solution straightforward.

Final Answer:
The finishing point of the marathon route is located 31 km North of the starting position.