A boy travels 4 km towards the south and then takes a right turn and travels another 3 km in that new direction. How far is he now from his original position and in which direction from the starting point is he located?

Introduction / Context:
This is a basic two step direction sense question where the final displacement forms a right angled triangle. The goal is to compute both the distance from the origin and the approximate direction of the final point. Such questions often rely on recognising simple Pythagorean triples and understanding that combining south and west displacements yields a south west resultant direction.

Given Data / Assumptions:

• The boy starts from a fixed initial position.
• He travels 4 km towards the south.
• He then takes a right turn and travels 3 km.
• Taking a right turn while initially facing south means he then travels towards the west.
• We assume straight paths and exact right angle turns.

Concept / Approach:
We place the starting point at (0, 0). Moving south decreases the y coordinate, and moving west decreases the x coordinate. After computing the final coordinates, we view the displacement vector as the hypotenuse of a right angled triangle whose legs are 3 km and 4 km. The length of this hypotenuse gives the straight line distance from the starting point, and the signs of the coordinates tell us that the direction lies in the south west quadrant.

Step-by-Step Solution:
Step 1: Start with coordinates (0, 0).Step 2: Moving 4 km south leads to the point (0, -4).Step 3: While facing south, a right turn leads to facing west. Travelling 3 km west changes the coordinates to (-3, -4).Step 4: The net displacement is therefore 3 km west and 4 km south from the origin.Step 5: The distance from the origin is the hypotenuse of a right angled triangle with sides 3 and 4, so distance = square root of (3^2 + 4^2) = square root of (9 + 16) = square root of 25 = 5 km.Step 6: Since both x and y coordinates are negative, the position is to the south west of the starting point.

Verification / Alternative check:
The numbers 3, 4 and 5 form a very common Pythagorean triple that appears in many reasoning and quantitative aptitude questions. Knowing this triple allows a quick mental check that the straight line distance must be 5 km when the perpendicular movements are 3 km and 4 km. A small sketch with a vertical line of 4 km downward and a horizontal line of 3 km to the left clearly shows a diagonal pointing to the south west direction.

Why Other Options Are Wrong:
Option A (6 km, south) incorrectly adds distances and ignores the westward movement. Option C (4 km, north) not only chooses the wrong distance but also the opposite vertical direction. Option D (5 km, north-west) has the correct distance but the wrong quadrant, because the movements were south and west, not north and west. Only option B, 5 km towards the south west, correctly represents the net displacement.

Common Pitfalls:
Students sometimes misinterpret the right turn when facing south, mistakenly thinking it leads to east rather than west. Another mistake is to treat 3 km and 4 km as distances along the same straight line and simply add them. Remember that when two moves are perpendicular, you should form a triangle and use the Pythagoras theorem to compute net displacement.

Final Answer:
The boy is finally 5 km away from his starting position in the south west direction, so the correct option is “5 km, south-west”.