5 men can complete a work in 12 days, and 6 women can complete the same work in 20 days. In how many days can 1 man and 1 woman together complete this work?

40 days

Given,

5M x 12 = 6W x 20

⇒ M = 2W

⇒ M : W = 2 : 1   (Efficiency)

⇒ Total work = 5(2) x 12 = 120 units,

⇒ Time required by 1 man and 1 woman to complete total work = \(\frac{120}{1(2) + 1(1)}\) = \(\frac{120}{3}\) = 40 days,  ..(\(\frac{Work}{Efficiency}\) = Time)