Let's solve this directional reasoning problem by carefully analyzing each statement and establishing the relative positions of the houses. We need to find the location of house C with reference to house A.

Analyzing the Given House Locations

We are given the following information about the locations of six houses A, B, C, D, E, and F:

• D is 60 m south of E.
• F is 40 m south of B.
• A is 30 m north of E.
• F is 50 m east of A.
• C is 50 m west of B.

Step-by-Step Solution to Find C Relative to A

We can use a coordinate system to visualize the relative positions. Let's place house A at the origin (0, 0) for reference. We'll consider East as the positive x-direction and North as the positive y-direction.

1. Locate A: A is at (0, 0).
2. Locate E relative to A: A is 30 m north of E, which means E is 30 m south of A. If North is +y, then South is -y. So, E is at (0, -30).
3. Locate D relative to E (and A): D is 60 m south of E. Since E is at (0, -30), D is at (0, -30 - 60) = (0, -90).
4. Locate F relative to A: F is 50 m east of A. If East is +x, then F is at (0 + 50, 0) = (50, 0).
5. Locate B relative to F (and A): F is 40 m south of B, which means B is 40 m north of F. F is at (50, 0). Moving 40 m north from F means adding 40 to the y-coordinate. So, B is at (50, 0 + 40) = (50, 40).
6. Locate C relative to B (and A): C is 50 m west of B. B is at (50, 40). Moving 50 m west from B means subtracting 50 from the x-coordinate. So, C is at (50 - 50, 40) = (0, 40).

Now we have the coordinates for A and C:

• A: (0, 0)
• C: (0, 40)

To find the location of C with reference to A, we look at the difference in their coordinates.

• x-difference: $0 - 0 = 0$. This means C is neither East nor West of A.
• y-difference: $40 - 0 = 40$. Since the y-coordinate of C (40) is positive and the positive y-direction represents North, C is 40 m North of A.

Let's summarize the positions we found using the coordinate method with A at (0,0):

From the table, comparing C (0, 40) and A (0, 0), we see C is located 40 units in the positive y-direction from A, which corresponds to 40 m North.

Location of C with Reference to A

Based on our calculations, house C is located 40 m North of house A.

Revision Table: Key Concepts

Additional Information on Spatial Reasoning

Spatial reasoning is a cognitive process that involves understanding, remembering, and manipulating spatial relationships between objects or points in space. In competitive exams, questions on spatial reasoning often involve:

• Directions (North, South, East, West, Northeast, Northwest, Southeast, Southwest).
• Distances.
• Relative positioning of people, objects, or places.
• Movement and displacement from a starting point.

Solving these problems often requires building a mental map or drawing a diagram/using a coordinate system to represent the information accurately. By breaking down complex descriptions into simpler steps and connecting the information logically, we can determine the final location or relationship.