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?

5 men can complete a work in 12 days. 6 women can complete the same work in 20 days.

Let's assume the efficiency of a man and a woman is 'M' and 'W' respectively.

$$5\times M \times 12 = 6\times W \times 20$$

$$M = 2W$$    Eq.(i)

Let's assume 1 man and 1 woman together complete this work in 'y' days.

$$5\times M \times 12 = 1\times (M+W) \times y$$

Put Eq.(i) in the above equation.

$$5\times 2W \times 12 = 1\times (2W+W) \times y$$

$$5\times 2W \times 12 = (3W)y$$

$$10 \times 4 = y$$

y = 40

So 1 man and 1 woman together complete this work in 40 days.