Given Information:
- Suraj walks 11 km towards east.
- Suraj takes a left turn and walks 12 km.
- Suraj takes another left turn and walks 6 km to reach the destination.

To Find:
The shortest distance between the start and end point.

Explanation:
To find the shortest distance between the start and end point, we need to determine the path Suraj took and calculate the distance between the start and end point using that information.

- Suraj walks 11 km towards the east. Let's assume this is the starting point (A).
- When Suraj takes a left turn, he would be heading towards the north. Let's assume this point as B.
- Suraj walks 12 km towards the north. Let's assume this point as C.
- When Suraj takes another left turn, he would be heading towards the west. Let's assume this point as D.
- Suraj walks 6 km towards the west. Let's assume this point as E.

Now, we need to calculate the shortest distance between the start point (A) and the end point (E).

Calculating the Shortest Distance:
To calculate the shortest distance, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, we have a right-angled triangle ABC, where AB represents the distance Suraj walked towards the east (11 km) and BC represents the distance Suraj walked towards the north (12 km).

Using the Pythagorean theorem, we can calculate the length of AC as follows:

AC² = AB² + BC²
AC² = 11² + 12²
AC² = 121 + 144
AC² = 265
AC ≈ 16.28 km

Now, we have another right-angled triangle ADE, where AD represents the distance Suraj walked towards the west (6 km) and DE represents the distance Suraj walked towards the north (12 km).

Using the Pythagorean theorem, we can calculate the length of AE as follows:

AE² = AD² + DE²
AE² = 6² + 12²
AE² = 36 + 144
AE² = 180
AE ≈ 13.42 km

Thus, the shortest distance between the start and end point is approximately 13.42 km.

Therefore, the correct answer is option B) 13 km.