From his house, Lokesh went 15 km to the North. Then he turned west and covered 10 km. Then he turned south and covered 5 km. Finally turning to the east, he covered 10 km. In which direction is he from his house?

To determine Lokesh's final direction from his house, let's analyze each step of his journey:

1. Going 15 km North:
- Lokesh starts from his house and moves 15 km in the North direction.

2. Turning West and covering 10 km:
- After moving 15 km North, Lokesh turns to his left (West) and covers a distance of 10 km.

3. Turning South and covering 5 km:
- Following the Westward direction, Lokesh turns to his left again (South) and covers a distance of 5 km.

4. Turning East and covering 10 km:
- After moving 5 km South, Lokesh turns to his left (East) and covers a distance of 10 km.

Now let's determine the final direction:

- Lokesh initially moved 15 km North, then turned West and covered 10 km.
- This means that he moved 15 km North and then moved 10 km West from that point.

So, the final position is 15 km North and 10 km West from his house.

To simplify this, we can use the concept of vectors.

- Moving North can be represented by a vector (0, 15) where the first value represents the East-West direction (0 means no movement in that direction) and the second value represents the North-South direction (15 means moving 15 km North).
- Turning West and covering 10 km can be represented by a vector (-10, 0) where the first value represents the East-West direction (-10 means moving 10 km West) and the second value represents the North-South direction (0 means no movement in that direction).
- Turning South and covering 5 km can be represented by a vector (0, -5) where the first value represents the East-West direction (0 means no movement in that direction) and the second value represents the North-South direction (-5 means moving 5 km South).
- Turning East and covering 10 km can be represented by a vector (10, 0) where the first value represents the East-West direction (10 means moving 10 km East) and the second value represents the North-South direction (0 means no movement in that direction).

Adding these vectors together:
(0, 15) + (-10, 0) + (0, -5) + (10, 0) = (0 + (-10) + 0 + 10, 15 + 0 + (-5) + 0) = (0, 10)

The resulting vector (0, 10) represents the final position of Lokesh from his house. The first value, 0, means no movement in the East-West direction, and the second value, 10, means moving 10 km North.

Therefore, Lokesh is 10 km North from his house, which corresponds to the direction North (option C).