Given:
Nishu starts from a fixed point and goes 15 km towards North.
After turning right, he goes 15 km.
Then he turns left and goes 10 m, again turns left and goes 15 m, and finally turns left and goes 15 m.

To find:
The distance of Nishu from his starting point.

Solution:
Let's assume Nishu's starting point as O.
Nishu moves 15 km towards the North and reaches point A.
After turning right, he moves 15 km and reaches point B.

Let's draw a diagram to visualize the path of Nishu:

```
15 km
O-------------------> A
|
|
| 15 km
|
|
B
/|\
/ | \
/ | \
/ | \
/ | \
10 m / 15 m \ 15 m
/ \
/ \
C D
```

After reaching point B, Nishu turns left and moves 10 m to reach point C.
Then he turns left again and moves 15 m to reach point D.
Finally, he turns left again and moves 15 m to reach point E.

Now, we need to find the distance between point E and point O to determine Nishu's distance from his starting point.

Let's apply the Pythagorean theorem to find the distance between points B and C:
BC² = 15² + 10²
BC = √(225 + 100)
BC = √325

Similarly, the distance between points C and D can be found using the Pythagorean theorem:
CD² = 15² + 10²
CD = √325

And, the distance between points D and E can also be found using the same method:
DE² = 15² + 15²
DE = √450

Now, to find the distance between point E and point O, we need to find the distance between points B and E first.

Let's consider triangle BDE:
BE² = BD² + DE²
BE² = (15 + √325)² + √450²
BE = √(225 + 30√325 + 325 + 450)
BE = √(1000 + 30√325)

Finally, to find the distance between point E and point O, we need to subtract the distance between point B and point O from BE:
OE = BE - BO
OE = √(1000 + 30√325) - 15

Calculating this value using a calculator, we get:
OE ≈ 9.87 km

Therefore, Nishu is approximately 9.87 km away from his starting point.

Hence, the correct option is (b) 10 km.