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?

30 days

X + Y = 12 days,

Let Y = a days

Let X = a -10 days

So, Y in a day = \(\frac{1}{a}\) 

and X in a day = \(\frac{1}{a - 10}\),

According to the question,

\(\frac{1}{a}\) + \(\frac{1}{a - 10}\) = \(\frac{1}{12}\)

⇒ \(\frac{2a -10}{a x a - 10a}\) = \(\frac{1}{12}\)

⇒ \( {a }^{ 2} \) - 10a = 24a - 120

⇒ \( {a }^{ 2} \) - 34a + 120 = 0

⇒ (a - 30)(a - 4) = 0

So, a = 30 or a = 4 (Not possible)

Therefore, Y can alone finish the work in 30 days.