$39$ persons can repair a tunnel in $12$ days working $10$ hours a day. In how many days will $30$ persons working $6$ hours a day complete the work?

We can use the work formula based on the Chain Rule:
$$M_1\times D_1\times H_1=M_2\times D_2\times H_2$$

Where:

* $M_1=39$, $D_1=12$, $H_1=10$
* $M_2=30$, $H_2=6$, and $D_2$ is the unknown number of days.

Substitute the given values into the equation:

$$39\times 12\times 10=30\times D_2\times 6$$

$$4680=180\times D_2$$

$$D_2=\frac{4680}{180}=\frac{468}{18}=26\text{ days}$$

Therefore, $30$ persons will complete the work in $26$ days.