If 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days, then 10 women complete it in ?

Solution(By Examveda Team)

$$\eqalign{ & {\text{According to the question,}} \cr & \Rightarrow {\text{4m}} + {\text{6w}} = 8{\text{ days}}.....{\text{(i)}} \cr & {\text{or}} \cr & \Rightarrow {\text{32m}} + 48{\text{w}} = 1{\text{ days}} \cr & \Rightarrow {\text{3m}} + 7{\text{w}} = 10{\text{ days}}.....{\text{(ii)}} \cr & {\text{or}} \cr & \Rightarrow {\text{30m}} + 70{\text{w}} = 1{\text{ day}} \cr & \therefore {\text{32m}} + {\text{48w}} = 30{\text{m}} + 70{\text{w}} \cr & \Rightarrow {\text{2m}} = 22{\text{w}} \cr & \Rightarrow {\text{m}} = 11{\text{w}} \cr & {\text{From (i)}} \cr & \Rightarrow {\text{4m}} = 44{\text{w}} \cr & \therefore \left( {{\text{44w}} + {\text{6w}}} \right) \times 8 = 10{\text{w}} \times x \cr & \Rightarrow {\text{50w}} \times 8 = 10{\text{w}} \times x \cr & \Rightarrow x = 40{\text{ days}} \cr} $$