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 ?

Let Gagan's efficiency be 1 unit. Naman does half the work in 4/5 the time, so Naman's efficiency = (1/2)/(4/5) = 5/8. Combined efficiency = 1 + 5/8 = 13/8. They complete the work in 16 days, so total work = 16 × 13/8 = 26 units. Gagan alone would take 26/1 = 26 days. The key is understanding relative efficiency from the given relationship.