Prabhu travels from his house to the house of his friend, covering a distance of 20 km in a straight line. After some time he leaves his friend house, turns to his right and travels 15 km to reach a park. After resting for a while, he again starts, turns to his right and travels 18 km to reach a petrol bunk. From there he once more turns to his right and covers a further distance of 15 km. Based on this information, how many more kilometres does he need to travel in a straight line to reach back to his home from his current position?

Introduction / Context:
This question is a classic example of a direction sense and displacement problem. Instead of only tracking how much total distance Prabhu walks, we are interested in where he finally lands with respect to his home. The task is to visualise his path step by step and then calculate how far his current position is from the starting point, that is, his home. Understanding such questions helps strengthen spatial reasoning, basic coordinate ideas, and the difference between path length and shortest straight line distance, which is also called displacement.

Given Data / Assumptions:

• Prabhu travels 20 km in a straight line from his house to the house of his friend.
• From his friend house he turns right and travels 15 km to reach a park.
• From the park he again turns right and travels 18 km to reach a petrol bunk.
• From the petrol bunk he again turns right and covers 15 km.
• All turns are right angle turns and all roads are assumed to be straight and on a flat plane.
• We assume he initially starts in the east direction for convenience, which does not affect the final distance calculation.

Concept / Approach:
To solve this, we imagine or sketch Prabhu path on a coordinate grid. We assume he first moves east, then apply each right turn to decide the new direction. By converting each move into horizontal and vertical components, we can track his final coordinates relative to the starting point. Once the final coordinate is known, the straight line distance from the origin can be found. In this particular case, because he ends up directly east or west of the starting point, the displacement can be read directly from the horizontal component, without using the Pythagoras theorem.

Step-by-Step Solution:
Step 1: Assume Prabhu starts from his home at the origin point, say (0, 0), and initially walks 20 km towards the east, reaching the friend house at (20, 0). Step 2: From the friend house he turns right. A right turn from east means he now faces south and walks 15 km, reaching the park at (20, -15). Step 3: From the park he again turns right. Facing south, a right turn makes him face west. He travels 18 km west and reaches the petrol bunk at (20 - 18, -15) which is (2, -15). Step 4: From the petrol bunk he once more turns right. Facing west, a right turn makes him face north, and he travels 15 km north to reach (2, -15 + 15) which is (2, 0). Step 5: His final position is (2, 0), while his home is still at (0, 0). Therefore, he is 2 km east of his home. Step 6: To reach home, he only needs to travel 2 km directly west in a straight line.

Verification / Alternative check:
An alternative way without coordinates is to notice that the three consecutive right turns form almost a rectangular loop for the 15 km sides. The north and south movements of 15 km cancel out each other. Along the east west line, he first went 20 km east, then effectively 18 km back towards the west, so the net result is that he is 2 km to the east of his home. Therefore, he must cover 2 km more to reach his home. This cross check confirms the coordinate method result.

Why Other Options Are Wrong:
The option 18 km is incorrect because it ignores the cancellation of some segments and mixes total distance walked with displacement. The option 21 km is wrong because it might come from subtracting or adding the wrong pair of distances. The option 23 km is incorrect as it assumes a mistaken net distance or uses total path length ideas instead of shortest distance. None of these values correspond to the actual horizontal separation of 2 km between his final point and his home.

Common Pitfalls:
A frequent mistake in such questions is to add all distances and assume that the result is the answer, which confuses total distance travelled with shortest straight line distance from the starting point. Another common error is mixing up the directions when turning right or left, especially after more than one turn. Forgetting that north cancels south and east cancels west when the magnitudes match is another key source of error. Drawing a neat diagram or using a simple coordinate approach helps avoid these pitfalls.

Final Answer:
The required straight line distance from his current position back to his home is 2 km.