A man is twice as fast as a woman and a woman is thrice as fast as a boy. If together, they can finish a work in 6 days, how long will a woman and a boy together take to finish the same work?

15 days

                 Man  :  Woman  :  Boy

Efficiency      6    :        3    :      1      

Total efficiency = 6 + 3 + 1 = 10

Total work = efficiency x No. of days = 10 x 6 = 60 

Time taken by a woman and a boy to complete this same work = \(\frac{Total\; work}{efficiency}\)

                                                                          = \(\frac{60}{4}\) = 15 days