In one-sixth of the time that B takes to complete a piece of work, A can complete half of the same work. If working together they take 16 days to complete the work, how much time shall B take to complete it alone ?

64 days

A + B = 16 days,

B x \(\frac{1}{2}\) = A x \(\frac{1}{6}\)

⇒ A = 3B

⇒ A : B = 3 : 1 (Efficiency)

 According to the question,

⇒ Total work = (3 + 1) x 16 = 64 units,  ..(Efficiency × Days = Total work)

⇒ Time taken by B = \(\frac{64}{1}\) = 64 days,   ..(\(\frac{Work}{Efficiency}\) = Time)

Hence, B alone takes 64 days to complete the work.