**Direction 16-20: Read the following information carefully and answer the given questions.**

**A $ B means A is to the north of B at a distance of either 4m or 9m.**

**A & B means A is to the west direction of B at a distance of either 3m or 12m.**

**A % B means A is to the south direction of B at a distance of either 4m or 9m.**

**A # B means A is to the east direction of B at a distance of either 3m or 12m.**

**A $# B means A is to the north-east of B.**

**A %# B means A is to the south-east direction of B.**

**B$A, C&B, D%C, D$&A, D&H&G, B$H, A&F, (CB>AF)**

**16.In which direction is C with respect to F?**

**a.North b. East c. North-East d. North-West e. None of these**

**17.What is the distance between D and G?**

**a.10 m b. 28 m c. 9m d. 15 m e. 14 m**

**18.What is the total distance between F and G?**

**a.5m b. 15m c. 4m d. 12m e. None of these**

**19.In which direction is B with respect to D?**

**a.North b. East c. North-East d. North-West e. None of these**

**20. If C & J, then what is the total distance between J and D. (It is given that AF=CJ)**

**a. 5m b. 15m c. 4m d. 12m e. None of these**

To solve the problem, let's break down the relationships and directions step by step.

### Understanding the Notations:

- **A $ B**: A is to the north of B at a distance of either 4m or 9m.
- **A & B**: A is to the west of B at a distance of either 3m or 12m.
- **A % B**: A is to the south of B at a distance of either 4m or 9m.
- **A # B**: A is to the east of B at a distance of either 3m or 12m.
- **A $# B**: A is to the north-east of B.
- **A %# B**: A is to the south-east of B.

Given the relationships and the positions:

### Relationships:

1. **B$A**: B is to the north of A (either 4m or 9m).
2. **C&B**: C is to the west of B (either 3m or 12m).
3. **D%C**: D is to the south of C (either 4m or 9m).
4. **D$&A**: D is to the north-west of A.
5. **D&H&G**: D is to the west of H, and H is to the west of G.
6. **B$H**: B is to the north of H (either 4m or 9m).
7. **A&F**: A is to the west of F (either 3m or 12m).
8. **CB > AF**: Distance CB is greater than the distance AF.

### Step-by-Step Solutions:

**16. In which direction is C with respect to F?**

- **A is west of F (A & F)**, and **C is west of B**.
- Since **B is north of A**, C will be to the **North-West of F** (depending on the distances, but it’s clear from the configuration that it cannot be just west or north).

**Answer: d. North-West**

**17. What is the distance between D and G?**

- **D is west of H**, and **H is west of G**.
- Since the directions and distances are not explicitly given in the question, the possible minimum distance could be calculated if we take the smallest possible distances for each:
  - Distance between D and H = 3m (smallest west direction).
  - Distance between H and G = 12m (smallest west direction).
  
  The distance between D and G would be $3m + 12m = 15m$.

**Answer: d. 15 m**

**18. What is the total distance between F and G?**

- To calculate the total distance between F and G, you need to consider both the horizontal and vertical distances.
- If F and G have a distance computed via vectors adding (considering both the west/east and north/south components), you would combine these distances.
  
  However, the relationship provided suggests possible minimum distances, so the answer is **None of these** if the provided options don’t match the computed values.

**Answer: e. None of these**

**19. In which direction is B with respect to D?**

- **D is to the south of C**, and **B is to the north of A**.
- **A is west of F**, and since **D is to the north-west of A**, B is likely to be in the **North-East** direction concerning D.

**Answer: c. North-East**

**20. If C & J, then what is the total distance between J and D?**

- Given **C & J** means **C is to the west of J**, and since **AF = CJ**, distances should match.
- Depending on the calculation for the distance:
  - If **AF = CJ**, then J and D should match the relationship as per provided distances.
  - Possible total distance between J and D can be **None of these** if computed distances don’t align exactly with the provided options.

**Answer: e. None of these** (If total distances differ from expected)

### Further Related Questions:

1. If F # H, what is the direction of F with respect to G?
2. What is the possible range of distance between B and A?
3. If J % G, what is the direction of D concerning J?
4. How does the direction of C from D affect the position of A?
5. Calculate the distance if B % G.

**Tip**: Always double-check the cardinal directions (north, south, east, west) and use vector addition if distances involve diagonal movements.

Explore the solution to a series of spatial relation and direction problems. Learn about directional notations like north, south, east, west, and their application in determining positions and distances. Suitable for Grade 7 students.

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