X and Y together can finish a piece of work in 15 days, while Y alone can finish it in 40 days. X alone can finish the work in:

Let the total work = W

Number of days in which X and Y together finish the work = 15 days

$$=$$>  Work done by X and Y together in 1 day = $$\frac{W}{15}$$

Number of days in which Y alone finish the work = 40 days

$$=$$>  Work done by Y alone in 1 day = $$\frac{W}{40}$$

$$=$$>  Work done by X alone in 1 day = $$\frac{W}{15}-\frac{W}{40}=\frac{5W}{120}=\frac{W}{24}$$

$$\therefore\ $$Number of days in which X alone finish the work = $$\frac{W}{\frac{W}{24}}=24$$ days

Hence, the correct answer is Option A