8 men or 10 boys can complete a work in 174 days. 12 men and 14 boys will complete the same work in how many days?

60 days

Given, 

8 Men x 174 = 10 Boys x 174,

⇒ M : B = 10 : 8 = 5 : 4 (Efficiency)

⇒ Total work = 8(5) x 174 = 6960 units   ..(Efficiency × Days = Total work)

⇒ Time required for 12 Men and 14 Boys to complete the whole work = \(\frac{6960}{12(5) + 14(4)}\) = \(\frac{6960}{116}\) = 60 days.   ..(\(\frac{Work}{Efficiency}\) = Time)