N₁ alone can do 20% of a piece of work in 6 days, N₂ alone can do 20% of the same work in 4 days, and N₃ alone can do 50% of the same work in 12 days. In how many days can they complete the work, if all of them work together ?

8 days

N₁ = \(\frac{1}{5}\)W = 6 days = 30 days,

N₂ = \(\frac{1}{5}\)W = 4 days = 20 days,

N₃ = \(\frac{1}{2}\)W = 12 days = 24 days,

⇒ Time required by N₁ + N₂ + N₃ to comlete the work = \(\frac{120}{4+6+5}\) = \(\frac{120}{15}\) = 8 days,    ..(\(\frac{Work}{Efficiency}\) = Time)