Aditi departs from her home and walks 38 m towards West and then turns right and walks 19 m. Now she turns right and walks 25 m. She then takes a left turn and walks 21 m. She then takes a left turn again and walks 38 m. She takes a final left turn and walks 25 m to stop at point X. How far is she from a pole which is 15 m North of her house? (Assume that all turns are 90 degree turns only.)

Correct Option: 51 m

To find the distance between Aditi's final position (point X) and the pole, we can trace her path step-by-step using a standard 2D coordinate system. Let us assume Aditi's home is at the origin point (0, 0), where:
- The positive x-axis represents East (+x)
- The negative x-axis represents West (-x)
- The positive y-axis represents North (+y)
- The negative y-axis represents South (-y)

Let's calculate the coordinates after each turn:

1. Start from home:
Initial coordinates:
$(0,0)$

2. Walks 38 m towards West:
Since West is in the negative x-direction, the coordinates become:
$(0-38,0)=(-38,0)$

3. Turns right and walks 19 m:
Facing West, a right turn points North (positive y-direction). The coordinates become:
$(-38,0+19)=(-38,19)$

4. Turns right and walks 25 m:
Facing North, a right turn points East (positive x-direction). The coordinates become:
$(-38+25,19)=(-13,19)$

5. Turns left and walks 21 m:
Facing East, a left turn points North (positive y-direction). The coordinates become:
$(-13,19+21)=(-13,40)$

6. Turns left and walks 38 m:
Facing North, a left turn points West (negative x-direction). The coordinates become:
$(-13-38,40)=(-51,40)$

7. Turns left and walks 25 m to stop at point X:
Facing West, a left turn points South (negative y-direction). The final coordinates of point X are:
$(-51,40-25)=(-51,15)$

8. Find the position of the pole:
The pole is located 15 m North of her house (0, 0). Therefore, the coordinates of the pole are:
$(0,15)$

9. Calculate the distance between point X and the pole:
Notice that both point X (-51, 15) and the pole (0, 15) have the same y-coordinate (15). This means they lie on the exact same horizontal line. The distance between them is the difference in their x-coordinates:
$\text{Distance}=|0-(-51\left)\right|=51\text{m}$
Thus, Aditi is exactly 51 m away from the pole.