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Fun Sports $\text{(FS)}$ provides training in three sports-Gilli-danda $\text{(G)}$, Kho-Kho $\text{(K)}$, and Ludo $\text{(L)}$. Currently it has an enrollment of $39$ students each of whom is enrolled in at least one of the three sports. The following details are known:

  1. The number of students enrolled only in $\text{L}$ is double the number of students enrolled in all the three sports.
  2. There are a total of $17$ students enrolled in $\text{G}$.
  3. The number of students enrolled only in $\text{G}$ is one less than the number of students enrolled only in $\text{L}$.
  4. The number of students enrolled only in $\text{K}$ is cqual to the number of students who are enrolled in both $\text{K}$ and $\text{L}$
  5. The maximum student enrollment is in $\text{L}$.
  6. Ten students enrolled in $\text{G}$ are also enrolled in at least one more sport.

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

  1. $18$
  2. $19$
  3. $17$
  4. $22$
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