A can do $\frac{2}{5}$ of a work in 12 days while B can do $66\frac{2}{3}\%$ of the same work in 16 days. They work together for 10 days. B alone will complete the remaining work in:

6 days

A = \(\frac{2}{5}\)W = 12 days = 30 days,

B = \(\frac{2}{3}\)W = 16 days = 24 days,

⇒ A + B worked for 10 days = (4 + 5) x 10 = 90 units ..(Efficiency × Days = Total work)

⇒ Remaining work = 120 - 90 = 30 units.

⇒ Time required by B to complete 30 units of work =  \(\frac{30}{5}\) = 6 days.   ..(\(\frac{Work}{Efficiency}\) = Time)