A # (12) B means A is 21m east of B
A * (03) B means A is 30m north of B
A % (24) B means A is 42m west of B
A @ (52) B means A is 25m south of B
Conditions: X # (93) Y; T * (42) U; R @ (61)Q; T # (03) S; P % (14) Q; W @ (61) X; Z * (01) Y; W % (45) U;
S*(80)R

Name the point which lies in a straight line?

The correct option is Y, X, R.

Step 1: Understand the Given Coded Directions and Distance Logic

Let's analyze how the symbols and numbers represent directions and distances:

1. A # (12) B means A is 21m east of B
Notice that the number in the bracket (12) is reversed to give 21, and the direction symbol # represents East.

2. A * (03) B means A is 30m north of B
The number (03) is reversed to give 30, and the direction symbol * represents North.

3. A % (24) B means A is 42m west of B
The number (24) is reversed to give 42, and the direction symbol % represents West.

4. A @ (52) B means A is 25m south of B
The number (52) is reversed to give 25, and the direction symbol @ represents South.

Step 2: Decode the Given Conditions

Now, let's decode each condition by reversing the digits of the distance values:

1. X # (93) Y ⇒ Reverse of 93 is 39. So, X is 39m East of Y.

2. T * (42) U ⇒ Reverse of 42 is 24. So, T is 24m North of U.

3. R @ (61) Q ⇒ Reverse of 61 is 16. So, R is 16m South of Q.

4. T # (03) S ⇒ Reverse of 03 is 30. So, T is 30m East of S.

5. P % (14) Q ⇒ Reverse of 14 is 41. So, P is 41m West of Q.

6. W @ (61) X ⇒ Reverse of 61 is 16. So, W is 16m South of X.

7. Z * (01) Y ⇒ Reverse of 01 is 10. So, Z is 10m North of Y.

8. W % (45) U ⇒ Reverse of 45 is 54. So, W is 54m West of U.

9. S * (80) R ⇒ Reverse of 80 is 08. So, S is 8m North of R.

Step 3: Analyze the Coordinates/Positions

Let's map out the relative position coordinates using Y as the reference origin (0, 0):

• Y = (0, 0)

• X is 39m East of Y ⇒ X = (39, 0)

• W is 16m South of X ⇒ W = (39, -16)

• Z is 10m North of Y ⇒ Z = (0, 10)

• W is 54m West of U ⇒ U is 54m East of W ⇒ U = (39 + 54, -16) = (93, -16)

• T is 24m North of U ⇒ T = (93, -16 + 24) = (93, 8)

• T is 30m East of S ⇒ S is 30m West of T ⇒ S = (93 - 30, 8) = (63, 8)

• S is 8m North of R ⇒ R is 8m South of S ⇒ R = (63, 8 - 8) = (63, 0)

• R is 16m South of Q ⇒ Q is 16m North of R ⇒ Q = (63, 0 + 16) = (63, 16)

• P is 41m West of Q ⇒ P = (63 - 41, 16) = (22, 16)

Step 4: Find the Straight Line Points

Let's examine the y-coordinates (horizontal lines) and x-coordinates (vertical lines) of the points:

Looking at the points along the horizontal line with y = 0:

• Y = (0, 0)

• X = (39, 0)

• R = (63, 0)

Since Y, X, and R all share the same y-coordinate (y = 0), the points Y, X, R lie in a single straight line along the East-West axis.