Raj leaves for his office in a car. He drives 15 km towards the north, then 10 km towards the west, then turns towards the south and covers 5 km, and further turns towards the east and moves 8 km. Finally he turns right and drives another 10 km. In which direction is he now from his starting point?

Introduction / Context:
This question describes Raj route with several directional changes and asks for his final direction from his starting point. The sequence of movements partly cancels out, so instead of focusing on the full path length, we should compute the net displacement by separating the horizontal and vertical components of his travel.

Given Data / Assumptions:

• Raj drives 15 km north.
• He then drives 10 km west.
• He then drives 5 km south.
• He then drives 8 km east.
• Finally, from facing east, he turns right and drives 10 km south.
• We must find his final direction from the starting point.

Concept / Approach:
We plot his movement on a coordinate grid. Take the starting point as (0, 0). Driving north increases y, south decreases y, east increases x, and west decreases x. After each segment, we update the coordinates. At the end, we look at the signs of x and y to decide the direction with respect to the starting point. For this question, only the final direction is needed, not the exact distance.

Step-by-Step Solution:
Start at (0, 0). Go 15 km north to reach (0, 15). Go 10 km west to reach (-10, 15). Go 5 km south to reach (-10, 10). Go 8 km east to reach (-2, 10). Facing east, a right turn leads south; go 10 km south to reach (-2, 0). Final coordinates are (-2, 0), which places Raj 2 km to the west of his starting point.

Verification / Alternative check:
Total vertical movement: 15 km north minus 5 km south minus 10 km south equals 0 km, so the net north south displacement is zero. Total horizontal movement: 10 km west minus 8 km east yields 2 km west. Therefore, Raj ends directly to the west of his starting position, confirming the coordinate calculation.

Why Other Options Are Wrong:
Option B: North would require a positive net vertical displacement, which is not present here.
Option C: South would require a negative net vertical displacement; again, net vertical displacement is zero.
Option D: East would require a positive net horizontal displacement, but the car ends to the west.
Option E: None of these is incorrect because West is a listed option and is correct.

Common Pitfalls:
A common mistake is to treat the last right turn from east as leading north instead of south. Another error is failing to account for all vertical movements and assuming Raj remains north of his starting point. Systematically summing horizontal and vertical components avoids such misinterpretations.

Final Answer:
Raj is finally in the West direction from his starting point.