Direction : Study the following information carefully and answer the questions…

Concept

This is a coded direction-and-distance puzzle: each symbol (@, #, &, %) fixes both a compass direction and a pair of possible distances between the two points it connects. When several such coded relations are chained together, plot every point on a standard coordinate axis (East = +x, North = +y) starting from a convenient origin, then use the given distance inequalities to pick the single valid distance out of each pair. Once every point's exact coordinates are known, the direction of any point from another follows directly from the sign of the x- and y-differences between them.

Application

1. Decode each symbol into a direction and a distance pair, remembering that “P(symbol)Q” always describes P's position relative to Q: & = North (4 m or 15 m), # = West (7 m or 18 m), % = South (7 m or 18 m), @ = East (4 m or 15 m).

2. From “J&K#L%M”: J&K means J is north of K (so JK = 4 m or 15 m); K#L means K is west of L (so KL = 7 m or 18 m); L%M means L is south of M (so LM = 7 m or 18 m).

3. From “B&N#M”: B&N means B is north of N (so BN = 4 m or 15 m); N#M means N is west of M (so MN = 7 m or 18 m).

4. Place K at the origin (0, 0). Since L is east of K, L = (KL, 0); since M is north of L, M = (KL, LM); since J is north of K, J = (0, JK).

5. Apply BN < MN < KL. The available values are BN ∈ {4, 15}, MN ∈ {7, 18}, KL ∈ {7, 18}; the only combination that satisfies BN < MN < KL is BN = 4 m, MN = 7 m, and KL = 18 m.

6. Apply JK > LM. The available values are JK ∈ {4, 15} and LM ∈ {7, 18}; the only combination that satisfies JK > LM is JK = 15 m and LM = 7 m.

7. Since N is west of M by MN, N = (M's x − MN, M's y) = (18 − 7, 7) = (11, 7). Since B is north of N by BN, B = (N's x, N's y + BN) = (11, 7 + 4) = (11, 11).

8. Comparing K(0, 0) with B(11, 11): K's x-coordinate is smaller than B's, so K lies west of B; K's y-coordinate is smaller than B's, so K lies south of B.

Cross-check

As an independent check, the displacement from B to K is (0 − 11, 0 − 11) = (−11, −11); a negative x-component together with a negative y-component corresponds exactly to the South-West direction, confirming the coordinate calculation above.

Hence, K lies to the South-West of B.