A girl walks 30 metres towards the south from her starting point. Then, turning to her right, she walks another 30 metres. After that she turns to her left and walks 20 metres. Finally, she turns to her left again and walks 30 metres. How far is she from her initial position and what is the straight line distance between the starting point and her final position?

Introduction / Context:
This is a classic direction sense and distance problem. Such questions appear frequently in reasoning sections of competitive examinations. They test spatial imagination, the ability to track right and left turns, and the skill of computing net displacement using simple geometry or coordinate style reasoning. The key objective is to determine how far the girl is from the starting point after several movements in different directions, not the total path length walked.

Given Data / Assumptions:

• The girl starts from an initial point which we can treat as the origin.
• She first walks 30 metres towards the south.
• She then turns right from facing south and walks 30 metres.
• Next she turns left and walks 20 metres.
• Finally she turns left again and walks 30 metres.
• All turns are perfect right angles unless specifically stated otherwise.
• We need the straight line distance between her starting position and her final position.

Concept / Approach:
The systematic way to solve direction sense questions is to imagine or sketch a coordinate grid. We choose east as the positive x direction and north as the positive y direction. Then we track each movement step by step, updating the coordinates. Right and left turns are interpreted relative to the current facing direction. Once we know the coordinates of the final point, the straight line distance from the origin can be found using the Pythagoras rule: distance = square root of (x^2 + y^2). For simple right angled movements, this usually produces integer distances.

Step-by-Step Solution:
Step 1: Assume the girl starts at point O with coordinates (0, 0), facing south for the first movement. Step 2: She walks 30 metres south, so her new position is (0, -30). Step 3: From facing south, a right turn means facing west. She walks 30 metres west to reach the point (-30, -30). Step 4: From facing west, a left turn means facing south. She now walks 20 metres south to point (-30, -50). Step 5: From facing south, another left turn means facing east. She walks 30 metres east to point (0, -50). Step 6: The final coordinates are (0, -50). So the horizontal displacement is 0 metres and the vertical displacement is -50 metres. Step 7: The straight line distance from the origin to the final point is therefore the magnitude of the vertical displacement, which is 50 metres.

Verification / Alternative check:
Instead of working with coordinates, we can track net horizontal and vertical movements. Vertically, she goes 30 metres south and later 20 metres south, with no northward motion, giving a total of 50 metres south. Horizontally, she first goes 30 metres west and later 30 metres east, which cancel out, resulting in zero net horizontal displacement. Hence the final position is exactly 50 metres south of the starting point, so the straight line distance between the two points is 50 metres, confirming the earlier calculation.

Why Other Options Are Wrong:

• Option A, 20 metres, confuses one of the intermediate legs with the overall displacement.
• Option B, 30 metres, may come from ignoring the 20 metre leg or misreading the path as a simple rectangle.
• Option D, 60 metres, looks like the sum of 30 and 30, which is incorrect because it ignores cancellation in the horizontal direction.
• Option E, 40 metres, is a random distractor with no relation to the actual Pythagoras computation for this path.

Common Pitfalls:
Learners often misinterpret right and left turns when facing different directions. For example, a right turn from south leads to west, not east. Another frequent mistake is to add distances directly rather than computing net displacement. Remember that average or resultant displacement depends on how far you end from where you started, not on the total path walked. Drawing a simple diagram or using coordinates significantly reduces the chance of error in such questions.

Final Answer:
The girl finishes 50 metres away from her starting point, directly to the south, so the required distance is 50 metres.