A man moves 24 metres in the south direction from his starting point. He then turns 90 degrees anticlockwise and moves another 7 metres. After this he takes a right turn and moves 3 metres and then moves 3 metres in the north direction. What is the straight line distance between his initial position and his final position?

Introduction / Context:
Here we have a direction sense question involving southward movement, an anticlockwise turn, and a couple of short segments. We are asked for the straight line distance between the starting and final positions, which is the net displacement. These questions assess whether a candidate can correctly interpret anticlockwise and clockwise turns relative to the current direction and then combine movements using basic geometry or coordinate reasoning.

Given Data / Assumptions:

• The man starts at a fixed point.
• He walks 24 metres towards the south.
• He then turns 90 degrees anticlockwise and moves 7 metres.
• Next he turns right and moves 3 metres.
• Finally he moves 3 metres towards the north.
• All turns are at right angles and distances are exact.
• We have to find the straight line distance between initial and final positions.

Concept / Approach:
We use a coordinate system: let the starting point be at (0, 0), with east as positive x and north as positive y. Moving south reduces y, moving east increases x, and so on. An anticlockwise turn means turning left when viewed from above. After updating the coordinates with each movement, we compute the displacement as the square root of (x^2 + y^2). Because the path involves a right-angle triangle pattern, the final distance often comes out as a simple Pythagorean number.

Step-by-Step Solution:
Step 1: Start at (0, 0). The man moves 24 metres south, so his new position is (0, -24). Step 2: From facing south, a 90 degree anticlockwise turn makes him face east. Walking 7 metres east moves him to (7, -24). Step 3: From facing east, a right turn makes him face south. Moving 3 metres south puts him at (7, -27). Step 4: He then moves 3 metres north, which changes y by +3, so his final position is (7, -24). Step 5: The coordinates of the starting point are (0, 0) and those of the final point are (7, -24). Step 6: The straight line distance between these points is square root of (7^2 + 24^2) = square root of (49 + 576) = square root of 625 = 25 metres.

Verification / Alternative check:
We can check net horizontal and vertical movement separately. Horizontally, the man only moves 7 metres east; no later movement changes his x coordinate, so net x displacement is 7 metres. Vertically, he walks 24 metres south and later 3 metres south, then 3 metres north, for a net vertical movement of 24 metres south. Therefore the displacement forms a right triangle with legs 7 and 24. The well known Pythagorean triple 7, 24, 25 confirms that the hypotenuse, which is the displacement, equals 25 metres.

Why Other Options Are Wrong:

• Option B, 30 metres, would require larger legs or incorrect addition of distances without using Pythagoras.
• Option C, 27 metres, can come from wrongly adding 24 and 3 instead of working with the squared components.
• Option D, 35 metres, is another arbitrary value that does not match the geometry of this triangle.
• Option E, 20 metres, ignores the full southward displacement and is not supported by the calculations.

Common Pitfalls:
One common mistake is misinterpreting anticlockwise from south as west instead of east. Another error is to simply add or subtract all distances ignoring direction and the Pythagoras theorem. Students should practice identifying classical right triangles like 3, 4, 5 or 7, 24, 25, which appear frequently in aptitude questions, to quickly verify their answers under exam pressure.

Final Answer:
The man ends up 25 metres away from his starting point, so the required distance is 25 metres.