Ankita travels 35 km towards the west from her original position, then takes a right turn and travels 50 km, and next she takes another right turn and travels 35 km in that new direction. After completing this path, how far is she now from her original starting position, measured as the straight line distance?

Introduction / Context:
In this question Ankita traces a path that forms three sides of a rectangle. We are asked how far she is from the starting point after two right turns and three straight segments. This is another displacement question where the net distance from the origin is different from the total distance travelled. Recognising the rectangular structure simplifies the problem.

Given Data / Assumptions:

• Ankita travels 35 km towards the west from the original position.
• She then takes a right turn and travels 50 km.
• Next she takes another right turn and travels 35 km.
• Right turns are 90 degree right angle turns relative to her current direction.
• All roads are straight and lie in a horizontal plane.

Concept / Approach:
We again use a coordinate system. Movements west and east affect the horizontal coordinate, while movements north and south affect the vertical coordinate. Because the first and third legs both have length 35 km and run in opposite horizontal directions, those horizontal components will cancel. The remaining displacement will then be along the vertical axis only, which makes the final distance equal to the length of that single vertical leg.

Step-by-Step Solution:
Step 1: Place the starting point at (0, 0). After moving 35 km west, Ankita is at (−35, 0). Step 2: Facing west, a right turn makes her face north. She then travels 50 km north, reaching (−35, 50). Step 3: From facing north, a second right turn makes her face east. She travels 35 km east, increasing the horizontal coordinate from −35 to 0, so she reaches (0, 50). Step 4: The starting position was (0, 0). The final position is (0, 50). Therefore, she is 50 km north of her original position.

Verification / Alternative check:
Observe that her 35 km west movement is exactly countered by a 35 km east movement later, resulting in no net east west displacement. Only the 50 km northward leg remains unbalanced, so her net displacement from the start is just 50 km north. Since the question asks how far she is from the original position, the answer is simply 50 km regardless of direction.

Why Other Options Are Wrong:
The options 75 km, 20 km, and 25 km result from mistaken addition or subtraction of the different legs, such as adding 35 km and 50 km directly or subtracting them in the wrong order. Those calculations fail to recognise that the west and east horizontal legs cancel, leaving only a single vertical leg of 50 km as the net displacement.

Common Pitfalls:
A typical error is to treat the path as a triangle and apply the Pythagoras theorem incorrectly to 35 km and 50 km, or to simply sum some of the distances. Another mistake is to forget that the last leg is in the opposite horizontal direction to the first leg, which leads to ignoring cancellation. Visualising the path as a three sided rectangle makes it easier to see that only one side does not get cancelled.

Final Answer:
Ankita is now 50 km away from her original starting position.