If the numbers of students enrolled in K and L are in the ratio 19:22, then what is the number of students enrolled in L?

Let 'x' be the number of students enrolled in all three sports. Then the number of students enrolled only in L = 2x

It is given that there are a total of 17 students enrolled in G. Also, ten students enrolled in G are also enrolled in at least one more sport. Hence, the number of students enrolled in only G = 17 - 10 = 7

The number of students enrolled only in G is one less than the number of students enrolled only in L. Hence, the number of students enrolled only in L = 7+1 

$$\Rightarrow$$ 2x = 8 

$$\Rightarrow$$ x = 4 

Let us assume that 'y' students are enrolled in K and L but not G. Then, the number of students enrolled only in K = y + 4

Let us assume that 'z' be the the number of students enrolled in G and K but not L. Then, the number of students enrolled G and L bot not K = 10 - 4 - z = 6 - z

It is given that a total of 39 students in the sports. 

7 + z + 4 + 6 - z + 8 + y + y + 4 = 39 

$$\Rightarrow$$ y = 5 

Number of students enrolled in G = 17 

Number of students enrolled in K = 9 + 4 + 5 + z = 18 + z

Number of students enrolled in L = 6 - z + 4 + 5 + 8 = 23 - z

It is given that the maximum student enrollment is in L.

$$\Rightarrow$$ 23 - z > 18 + z

$$\Rightarrow$$ 2z < 5

$$\Rightarrow$$ z < 2.5 

Therefore, we can say that z can take three values = {0, 1, 2}

It is given that the numbers of students enrolled in K and L are in the ratio 19:22.

$$\dfrac{18+z}{23-z} = \dfrac{19}{22}$$

z = 1 which is a possible solution as well. 

In this case the number of students enrolled in L = 23 - z = 23 - 1 = 22. Hence, option C is the correct answer.