In 4/5 time, Naman can do half work of Gagan. When both of them are working together, then complete the entire work in 16 days. Find out the time taken by Gagan to complete the whole work done alone.

26 days

Given, 

⇒ Naman x \(\frac{4}{5}\) = Gagan x \(\frac{1}{2}\)

⇒ 8 x Naman = 5 x Gagan

⇒                    Naman : Gagan 

⇒ Efficiency       5        :   8

⇒ Total work = (5 + 8) x 16 = 208 units,     ..(Efficiency × Days = Total work)

⇒ Time taken by Gagan to complete the work alone = \(\frac{208}{8}\) = 26 days.