6 men and 10 boys, as well as 2 men and 20 boys can finish the same work in 12 days. In how many days will 10 boys finish the same work?

As we know, 

Total work = Efficiency $$\times\ $$ time taken

According to question, 

(6 men + 10 boys) $$\times\ $$12 = (2 men + 20 boys) $$\times\ $$12

6m - 2m = 20b - 10b

4m = 10b

$$\frac{m}{b}=\frac{5}{2}$$

Efficiency of men = 5, Efficiency of boys = 2

Total work = $$\left(6\times5\ +\ 10\times2\right)\times\ 12=600\ units$$

Time taken = $$\frac{\left(Total\ work\right)}{Efficiency\times\ number\ of\ boys}$$

$$\frac{600}{2\times10}=30\ days$$

Hence, Option D is correct.