Ravi's house is to the west of Ankit's house, and Lavi's house is to the north of Ankit's house. In which direction is Lavi's house located with respect to Ravi's house?

Introduction / Context:
This is a straightforward relative position problem involving three houses. Once we fix one house as a reference point, the positions of the other two can be represented on a simple grid. We then determine the direction of one house as seen from another by comparing their relative coordinates. Such problems are fundamental in direction sense topics and help in building a strong base for harder puzzles.

Given Data / Assumptions:

• Ravi's house is to the west of Ankit's house.
• Lavi's house is to the north of Ankit's house.
• We are asked for the direction of Lavi's house relative to Ravi's house.
• All directions follow the standard compass with north up and east to the right.

Concept / Approach:
We place Ankit's house at the origin of a coordinate system for convenience. Since Ravi's house is to the west of Ankit's house, we place Ravi's house on the negative side of the x axis. Since Lavi's house is to the north of Ankit's house, we place Lavi's house on the positive side of the y axis. The relative direction of Lavi's house from Ravi's house is obtained by drawing a line from Ravi's coordinate to Lavi's coordinate and reading off the resulting quadrant, which in this case is north east.

Step-by-Step Solution:
Step 1: Place Ankit's house at the origin (0, 0) for reference.Step 2: Ravi's house is to the west of Ankit's house. So if we take one unit of distance for simplicity, Ravi's house could be at (-1, 0).Step 3: Lavi's house is to the north of Ankit's house. So Lavi's house could be at (0, 1).Step 4: From Ravi's point of view, we need the direction from (-1, 0) to (0, 1).Step 5: To go from (-1, 0) to (0, 1), we move one unit east (increasing x from -1 to 0) and one unit north (increasing y from 0 to 1).Step 6: A combined movement of north and east corresponds to the diagonal direction north east.

Verification / Alternative check:
Visualising on a compass, imagine Ankit's house at the centre. Ravi's house lies to the left (west) of this centre and Lavi's house lies above (north) of this centre. Connecting Ravi's point on the left to Lavi's point above forms a line that slopes upward to the right, which is the north east direction from Ravi to Lavi. This alignments confirms the coordinate based reasoning.

Why Other Options Are Wrong:
Option A (South-West) would be the reverse direction from Lavi to Ravi, not from Ravi to Lavi. Option C (North-West) would require Lavi's house to be farther west than Ravi's house, which is not the case. Option D (South-East) mixes the vertical direction incorrectly because we clearly move northward from Ravi to Lavi, not southward. Only option B correctly states that Lavi's house is to the north east of Ravi's house.

Common Pitfalls:
Students sometimes confuse the direction between two points with its reverse. It is important to carefully read which point is considered the reference. Another common issue is thinking in a relative way but forgetting that moving east from a western point and north from a southern point produces a north east resultant direction. Drawing a quick L shaped arrow from Ravi to Lavi usually settles the matter.

Final Answer:
With respect to Ravi's house, Lavi's house is located in the north east direction, so the correct option is “North-East”.