A can complete a work in 16 days. B can complete the same work in 8 days. If both of them come together, then in how many days can they complete the same work?

$5\frac{1}{3}$days

Let the total work = 16 (LCM of time 16 & 8)

Total work = Efficiency × time

Efficiency of A = \(\frac{Total\;work}{time}\) =  \(\frac{16}{16}\) = 1w/d

Efficiency of B = \(\frac{Total\;work}{time}\) =  \(\frac{16}{8}\) = 2w/d

If A & B work together,

Efficiency of A + B = 3 w/d

Time to finish the work = \(\frac{Total\;work}{total\;efficiency}\) = \(\frac{16}{3}\) = 5\(\frac{1}{3}\) days