16 men or 24 women can do a piece of work in 20 days. The no. of days needed to complete the job if 20 men and 30 women are employed to do the same piece of work is 

16 men do work in 20 days

16 men do $\frac{1}{20}$th work in one day

1 men does $\frac{1}{320}th$work in 1 day

20 men do $\frac{20}{320}th$work in 1 day

Similary, 30 women do $\frac{30}{480}th$work in 1 day

Now 20 men and 30 women together do $=\frac{1}{16}+\frac{1}{16}=\frac{2}{16}$

$=\frac{1}{8}$work in 1 day

$\therefore$ Together they do work in 8 days.