Working 9 hours a day, 12 persons complete a work in 25 days. Working 6 hours a day, 15 persons can do the same work in.

The correct option is 30 days.

To find the number of days required to complete the work, we can use the concept of "Man-Hours" or the work equivalence formula:

$$M_1\times D_1\times H_1=M_2\times D_2\times H_2$$

Where:
- $M_1$ is the initial number of persons = 12
- $D_1$ is the initial number of days = 25
- $H_1$ is the initial working hours per day = 9
- $M_2$ is the new number of persons = 15
- $D_2$ is the new number of days (which we need to find)
- $H_2$ is the new working hours per day = 6

Substitute the given values into the formula:

$$12\times 25\times 9=15\times D_2\times 6$$

Now, calculate the left side of the equation:

$$12\times 25\times 9=300\times 9=2700$$

Now, set up the equation to solve for $D_2$:

$$2700=90\times D_2$$

Divide both sides by 90 to find $D_2$:

$$D_2=\frac{2700}{90}=30$$

Thus, 15 persons working 6 hours a day can complete the same work in 30 days.