Naman does half the work as Gagan in 4/5 the time. If together they take 16 days to complete a piece of work, then how long will it take Gagan to complete the work?

$$\eqalign{ & \frac{{{\text{Naman}} \times 4}}{{\frac{1}{2}}} = \frac{{{\text{Gagan}} \times 5}}{1} \cr & \frac{{{\text{Naman}}}}{{{\text{Gagan}}}} = \frac{5}{8} \cr & {\text{Total work}} = 16 \times \left( {5 + 8} \right) = 16 \times 13 \cr & {\text{Time taken by Gagan}} = \frac{{16 \times 13}}{8} = 26{\text{ days}} \cr} $$