3 men and 5 women together can complete a work in 6 days, whereas 4 men and 9 women together can do it in 4 days. How many women are required to do the same work in 7 days?

12

3M + 5W = 6 days,

18M + 30W         ..(1)       (Multiplied by 6 to get it done in 1 day)

4M + 9W = 4 days,

16M + 36W         ..(2)       (Multiplied by 4 to get it done in 1 day)

Now, (1) - (2), we get

⇒ 2M = 6W

⇒ M : W = 6 : 2 = 3 : 1 (Efficiencies)

Putting efficiency in equation (1), and we get the total work,

⇒ [18 (3) + 30(1)] = 84 units.

Hence number of Woem needed to complete the work in 7 days = \(\frac{84}{W(1)}\) = 7 days,

⇒ W = 12