A can do a piece of work alone in 40 days. A and B together can do the same work in 10 days. C is 50% less efficient than B. In how many days can A and C together complete the same work?

16 days

A = 40 days, A + B = 10 days,

⇒ A + B = 4,  (Efficiency)

⇒ 1 + B = 4,

⇒ B = 3,

C is 50% less efficient, 

B : C = 3 : 1.5,

⇒ Time required by A + C to complete the total work = \(\frac{40}{1+1.5}\) = \(\frac{40}{2.5}\) = 16 days,     ..(\(\frac{Work}{Efficiency}\) = Time)