If one man or two women or three boys can do piece of work in 55 days, then one man, one woman and one boy will do it in how many days?

1 man = 2 women = 3 boys

Therefore, 1 man + 1 woman + 1 boy

= \( \Large 3 boys + \frac{3}{2}boys+1 boy = \frac{11}{2} boy \)

Boys   Days
3          55
\( \Large \frac{11}{2} \)   x

=> \( \Large \frac{x}{55} = \frac{5}{\frac{11}{2}} \)

=>\( \Large x = \frac{3 \times 2}{11} \times 55 = 30 \  days \)