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:

24 days

X + Y = 15 days,

Y = 40 days,

⇒ X + Y = 8,  (Efficiency)

⇒ X + 3 = 8,

⇒ X = 5,

⇒ Time required by X to complete the work alone = \(\frac{120}{5}\) = 24 days,   ..(\(\frac{Work}{Efficiency}\) = Time)