In the given notation, $P@Q$ means $P$ is East of $Q$ and the distance between $P$ and $Q$ is either $4 ext{ m}$ or $15 ext{ m}$. $P#Q$ means $P$ is West of $Q$ and the distance between $P$ and $Q$ is either $7 ext{ m}$ or $18 ext{ m}$. $P&Q$ means $P$ is North of $Q$ and the distance between $P$ and $Q$ is either $4 ext{ m}$ or $15 ext{ m}$. $P%Q$ means $P$ is South of $Q$ and the distance between $P$ and $Q$ is either $7 ext{ m}$ or $18 ext{ m}$. Given the relations: - $J&K#L%M$ - $B&N#M$ - $BN

Question

In the given notation, $P@Q$ means $P$ is East of $Q$ and the distance between $P$ and $Q$ is either $4 	ext{ m}$ or $15 	ext{ m}$. $P#Q$ means $P$ is West of $Q$ and the distance between $P$ and $Q$ is either $7 	ext{ m}$ or $18 	ext{ m}$. $P&Q$ means $P$ is North of $Q$ and the distance between $P$ and $Q$ is either $4 	ext{ m}$ or $15 	ext{ m}$. $P%Q$ means $P$ is South of $Q$ and the distance between $P$ and $Q$ is either $7 	ext{ m}$ or $18 	ext{ m}$.

Given the relations:
- $J&K#L%M$
- $B&N#M$
- $BN < MN < KL$
- $JK > ML$

If $X$ is $11 	ext{ m}$ West of $B$, what is the distance between $X$ and $J$?

Accepted Answer

**Solution:**

1. Understand the notation:
   - $P@Q$: $P$ is East of $Q$ with distance either $4 	ext{ m}$ or $15 	ext{ m}$.
   - $P#Q$: $P$ is West of $Q$ with distance either $7 	ext{ m}$ or $18 	ext{ m}$.
   - $P&Q$: $P$ is North of $Q$ with distance either $4 	ext{ m}$ or $15 	ext{ m}$.
   - $P%Q$: $P$ is South of $Q$ with distance either $7 	ext{ m}$ or $18 	ext{ m}$.

2. Given relations:
   - $J&K#L%M$ means:
     - $J$ is North of $K$ (distance 4 or 15 m)
     - $K$ is West of $L$ (distance 7 or 18 m)
     - $L$ is South of $M$ (distance 7 or 18 m)

- $B&N#M$ means:
     - $B$ is North of $N$ (distance 4 or 15 m)
     - $N$ is West of $M$ (distance 7 or 18 m)

3. Inequalities given:
   - $BN < MN < KL$
   - $JK > ML$

4. $X$ is $11 	ext{ m}$ West of $B$.

5. To find the distance between $X$ and $J$, consider the relative positions:
   - Since $X$ is West of $B$ by $11 	ext{ m}$, and $B$ is North of $N$, which is West of $M$, and $J$ is North of $K$, which is West of $L$, which is South of $M$, the points form a spatial arrangement.

6. Using the given distances and inequalities, the only feasible distance between $X$ and $J$ that fits the constraints is $4 	ext{ m}$.

**Answer:** $4 	ext{ m}$

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