In the following questions, the symbols #, &, @ and \$ are used with the following meanings as illustrated below. Study the following information and answer the given questions: Note: The directions which are given indicates exact directions. P#Q - P is in the south direction of Q. P@Q - P is in the north direction of Q. P&Q - P is in the east direction of Q.
P\$Q - P is in the west direction of Q. P£QS- P is the mid-point of QS vertically. Note- For southeast direction it used to be written as P#&Q and so on… When it is given that the Car honks once then it will be considered as the car taken a left turn and if it is given as the car honks twice then it will be considered as the car takes a right turn. Point S is &15m of point B. Point J is @33m of point S. Point K is @25m of point B. Point L is
$20m of point K. Point Q is #40m of point L. Point F is &40m point Q. Point E£DF. Point D is @30m of Point F.
If Point U is #15m of point B (U is 15m south of B), then what is the position of U with respect to F?

Question

Accepted Answer

**Solution:**

1. Place point B at the origin (0,0) for reference.

2. From B:
   - S is 15m east: S(15, 0)
   - K is 25m north: K(0, 25)
   - U is 15m south: U(0, -15)

3. From K:
   - L is 20m west: L(-20, 25)

4. From L:
   - Q is 40m south: Q(-20, -15)

5. From Q:
   - F is 40m east: F(20, -15)

6. From F:
   - D is 30m north: D(20, 15)

7. E is midpoint vertically between D and F, so E lies at (20, 0).

8. Now, find U's position relative to F:
   - Coordinates of U: (0, -15)
   - Coordinates of F: (20, -15)

9. Calculate the relative position:
   - Horizontal difference: 0 - 20 = -20 (U is 20m west of F)
   - Vertical difference: -15 - (-15) = 0 (same latitude)

10. So, U is 20m west of F, i.e., $U$ is $20m$ to the west ($$\$) of $F$.

But the options do not have $\$, 20m$ as correct. Let's re-check the question carefully.

Wait, the question asks for position of U with respect to F.

Coordinates:
- F(20, -15)
- U(0, -15)

Distance between F and U:
- Horizontal distance = 20m
- Vertical distance = 0m

So, U is exactly 20m west of F.

Option (d) is "$, 20 m" which matches this.

But the answer key says (a) @, 24m is correct.

Check if we made any mistake.

Re-examine the coordinates:
- B(0,0)
- S(15,0)
- J is 33m north of S: J(15,33)
- K is 25m north of B: K(0,25)
- L is 20m west of K: L(-20,25)
- Q is 40m south of L: Q(-20,-15)
- F is 40m east of Q: F(20,-15)
- D is 30m north of F: D(20,15)
- E is midpoint vertically between D and F: E(20,0)
- U is 15m south of B: U(0,-15)

Now, find the vector from F to U:
- x difference: 0 - 20 = -20 (west)
- y difference: -15 - (-15) = 0

Distance = 20m west.

So, U is $20m$ west of F.

Therefore, the correct option is (d) "$, 20 m".

**Answer:** (d) $, 20 m

Answer

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