To complete a wall, X takes 50 percent more time than Y. If together they complete the wall in 15 days, then how much time will X alone take to complete it?

37.5 days

Given,

X takes 50 percent more time than Y.

Efficiency α \(\frac{1}{Time}\)

Therefore, 

⇒ X : Y = 2 : 3 (Efficiency)

⇒ X + Y completes a work in 15 days =(2 + 3) x 15 = 75 units.   ..(Efficiency × Days = Total work)

⇒ Time required by X to complete the work alone = \(\frac{75}{2}\) = 37.5 days.     ..(\(\frac{Work}{Efficiency}\) = Time)