Ravi starts walking from his house and goes 3 km towards the east to reach a bus stop. From the bus stop he boards a bus which goes straight in a direction towards his right for 4 km to reach his school. What is the straight line (crow flight) distance between his house and his school?

Introduction / Context:
This question is a classic direction and distance problem in which a person moves along two perpendicular directions. The story talks about Ravi walking from his home to a bus stop and then travelling by bus to his school. We are asked to find the straight line distance between the home and the school, which is often referred to as crow flight distance in aptitude questions.

Given Data / Assumptions:

• Ravi walks 3 km east from his house to reach the bus stop.
• At the bus stop he is facing east along his walking direction.
• The bus then moves straight towards his right for 4 km to reach the school.
• A right turn from facing east takes him towards the south.
• We assume the earth surface is locally flat and use standard north south east west axes.

Concept / Approach:
We can think of Ravi's movements as forming the two perpendicular legs of a right angled triangle. Walking east from home to the bus stop provides one horizontal leg, and the bus moving southwards gives a vertical leg. The crow flight distance between his home and school is the hypotenuse of this right angled triangle. The Pythagorean theorem is used to compute the length of this hypotenuse from the two perpendicular sides of 3 km and 4 km.

Step-by-Step Solution:
Step 1: Place Ravi's house at the origin (0, 0) on a coordinate plane with east as positive x and north as positive y.Step 2: After walking 3 km east, the bus stop is at (3, 0).Step 3: At the bus stop Ravi is facing east. A right turn from east means facing south.Step 4: The bus now travels 4 km south, so the school is at (3, −4).Step 5: The displacement from the house (0, 0) to the school (3, −4) is a right angled triangle with legs of 3 km east and 4 km south.Step 6: By the Pythagorean theorem, the distance d between home and school is d = √(3^2 + 4^2) = √(9 + 16) = √25 = 5 km.

Verification / Alternative check:
We can confirm the result by recognising that 3, 4, and 5 form a very common Pythagorean triple. Whenever the horizontal and vertical legs are 3 units and 4 units, the hypotenuse is 5 units. Because the movements are purely east and south with no diagonal segments, the crow flight distance must be the hypotenuse, and 5 km is the only value that satisfies this relationship. This confirms that the school is 5 km away from the house in a straight line.

Why Other Options Are Wrong:
The option 1 km is far too small and does not fit any reasonable combination of 3 km and 4 km perpendicular legs. The option 7 km is larger than the sum of the legs and cannot be the hypotenuse of a right angled triangle of 3 km and 4 km. The option 12 km is simply the sum of 3 and 9 or other miscalculations and is not supported by the geometry. The value 4 km corresponds to only one of the legs and therefore is not the crow flight distance between two endpoints of the path.

Common Pitfalls:
A frequent mistake is to add the two distances, 3 km and 4 km, and assume that 7 km is the answer, ignoring the fact that the two legs are perpendicular. Another common error is misinterpreting right and left and drawing a wrong orientation, which changes the coordinates entirely. Drawing a simple right angled triangle and labelling the legs makes it easier to see that the hypotenuse must be computed using the square root of the sum of squares of the two legs.

Final Answer:
The straight line or crow flight distance between Ravi's house and his school is 5 km.