6 men or 2 women or 4 boys can finish a work in 77 days. How many days will 1 man, 1 woman and 1 boy together take to finish the same work?

84

6M = 2W = 4B

⇒ Total work = 6(2) x 77 = 924 units.   ..(Efficiency × Days = Total work)

⇒ Time taken by 1M + 1W + 1B to complete total work = \(\frac{924}{1(2)+1(6)+1(3)}\) = \(\frac{924}{11}\) = 84 days.    ..(\(\frac{Work}{Efficiency}\) = Time)