Eighteen men can complete a work in 14 days. Three women do as much work as two men. Five men and six women started the work and continued for 4 days. Subsequently 3 more men joined the group. In how many total days was the work completed?

22

Given,

18 Men can complete a work in 14 days.

⇒ 3 women = 2 Men

Therefore, 

⇒ M : W = 3 : 2 (Efficiency)

⇒ Total work = 18 (3) x 14 = 756 units   ..(Efficiency × Days = Total work)

⇒ So, 5 men and 6 women worked for 4 days = (5(3) + 6(2)) x 4 = 180 units.

⇒ Remaining work = 756 - 180 = 648 units. 

⇒ 3 more joined, and now time taken by 8 men and 6 women to complete remaining work is =  \(\frac{648}{8(3) + 6(2)}\) = \(\frac{648}{36}\) = 18 days.     ..(\(\frac{Work}{Efficiency}\) = Time)

⇒ Therefore, total time taken to complete the whole work = 18 + 4 = 22 days.