X takes 10 days less than the time taken by Y to finish a piece of work. X and Y together can do it in 12 days. In how many days Y alone can finish the work?

Let the time taken by X = a - 10

The time taken by Y = a

Then, 

Work done by X = $$\frac{1}{a-10}$$

Work done by Y = $$\frac{1}{a}$$

According to question : 

$$\frac{1}{a}+\frac{1}{a-10}=\frac{1}{12}$$

$$\frac{2a-10}{a^2-10a}=\frac{1}{12}$$

$$a^2-34a+120=0$$

$$\left(a-30\right)\left(a-4\right)=0$$

$$a=30,\ 4$$

a = 4(a should be greater than 10)

So, a = 30

Time taken by Y alone to finish the work = 30 days

Hence, Option D is correct.