A can do 1/3 of a work in 30 days, B can do 2/5 of the same work in 24 days. They worked together for 20 days. C complete the remaining work in 8 days. Working together A, B and C will complete the same work in:

Answer: Option D

⇒ A can do $$\frac{1}{3}$$ of a work in 30 day
⇒ A completed work in 90 days
⇒ B can do $$\frac{2}{5}$$ of the same work in 24 days
⇒ B can completed work in 60 days
⇒ Let the total work = LCM (90, 60) = 180 unit
⇒ Efficiency of A = 3 unit/day
⇒ Efficiency of B = 2 unit/day
⇒ They both worked for 20 days, work done in 20 days = 20 × 5 = 100 unit
⇒ Remaining work = 180 - 100 = 80 unit
⇒ Remaining work done by C in 8 days
⇒ Efficiency of C = 10 unit/day
⇒ Efficiency of (A + B + C) = 15 unit/day
⇒ Work completed = $$\frac{180}{15}$$ = 12 days
∴ If all worked together, the work complete in 12 days.