Two vans X and Y start from the same point. X travels 5 km West, then turns to its left and travels 3 km. Y travels 13 km South, then turns West and travels 5 km, then turns to its left and travels 7 km. Where is Y with respect to X now?

Let's establish the common starting point at coordinates (0,0).
Movement of Van X:

Travels 5 km West →(−5,0)

Turns left (South) and travels 3 km →(−5,−3)
Final Position of X = (−5,−3)

Movement of Van Y:

Travels 13 km South →(0,−13)

Turns West and travels 5 km →(−5,−13)

Turns left (which is South while facing West) and travels 7 km →(−5,−13−7)=(−5,−20)
Final Position of Y = (−5,−20)

Relative Position:
Both X and Y share the same X-coordinate (−5).
The distance difference along the Y-axis is:

Y
X
​
−Y
Y
​
=−3−(−20)=17 km
Since Y is at −20 and X is at −3, Y is located exactly 17 km South of X.