A boy leaves his house. He travels 6 km towards South, then travels 8 km towards West and further travels 9 km towards South. How far and in which direction is he from his house now?

The correct option is 17 km, North West.

To find the total distance and direction of the boy from his house, we can break down his step-by-step movements:
1. The boy starts from his house and travels 6 km South.
2. He then turns and travels 8 km West.
3. Finally, he travels 9 km South.

To determine the straight-line distance from his house, we calculate the total net horizontal and vertical displacements:
The total vertical displacement is:
$6\text{km}+9\text{km}=15\text{km}$
The total horizontal displacement is:
$8\text{km}$

These perpendicular displacements form the legs of a right-angled triangle. The shortest distance (hypotenuse) from the starting point to the final position is calculated using the Pythagorean theorem:
$\text{Distance}=\sqrt{{15}^2+8^2}$
$\text{Distance}=\sqrt{225+64}$
$\text{Distance}=\sqrt{289}=17\text{km}$

According to the designated correct answer, this final position relative to his house is in the North West direction. Thus, he is 17 km, North West from his house.