24 women and 9 men can complete a certain piece of work in 18 days. Each women takes twice the amount of time taken by a man to finish the work. In how many days can only 9 men finish the same work?

42

24W + 9M = 18 days,

                  Man : Women

Time             1   :   2

Efficiency      2    :   1       (Efficiency α \(\frac{1}{Time}\))

⇒ Total work = [24(1) + 9(2)] x 18 = 42 x 18 = 756 units,    ..(Efficiency × Days = Total work)

⇒ Time required by 9 Man to complete the total work = \(\frac{756}{9(2)}\) = \(\frac{756}{18}\) = 42 days.     ..(\(\frac{Work}{Efficiency}\) = Time)