Person A can do one-fifth of the work in 3 days, while B's efficiency is half of that of A. In how many days A and B working together can do half of the work ?

5

B's efficiency is half of that of A         ..(Given)

therefore,            A  :  B

⇒ Efficiency         2  :  1 

⇒  A can complete\(\frac{1}{5}\)th of the work in 3 days = (2 x 3) = \(\frac{1}{5}\) x W

⇒ Total work = 30 units.

⇒ Now, no. of days in which A and B working together can do half of the work is ⇒ \(\frac{30}{2}\) x \(\frac{1}{(2+1)}\) = 5 days.