Three men and 4 women can do a piece of work in 7 days,

Solution

M D = M D ⇒ (3 men + 4 women) × 7 = (2 men + 1 women) × 14 ⇒ (3 men + 4 women) = (2 men + 1 women) × 2 ⇒ 3 men + 4 women = 4 men + 2 women ⇒ 2 women = men ⇒ (women ∶ men) = 1 : 2 ⇒ Efficiency Ratio of (women ∶ men) = 1 ∶ 2 ⇒ Total Work = Efficiency × Time ⇒ (3 men + 4 women) × 7 = (2 men + 1 women) × 14 ⇒ (3 × 2 + 4 × 1) × 7 = (2 × 2 + 1 × 1) × 14 = 70 ⇒ Total Work = 70 ⇒ number of days to complete the work by 7 women = Total work/Efficiency ⇒ 70/(7 × 1) ⇒ 10 days