A and B together can do a piece of work in 12 days, while A alone can complete the same work in 18 days. How long will B alone take to complete the work?

36 days

A + B = 12 days, A = 18 days,

⇒ A + B = 3  (Efficiency)

⇒ 2 + B = 3,

⇒ B = 1,

⇒ Time required for B to complete the work = \(\frac{36}{1}\) = 36 days,  ..(\(\frac{Work}{Efficiency}\) = Time)