Sixteen men and twelve women can complete a work in 8 days, if 20 men can complete the same work in 16 days, in how many days 16 women can complete the same piece of work ?

Let work done by 1 man be $$x$$ and 1 woman be $$y$$

Now, 16 men and 12 women complete work in 8 days.

=> $$16x + 12y = \frac{1}{8}$$ ---------Eqn(i)

Also, $$20x = \frac{1}{16}$$

=> $$16x = \frac{1}{20}$$

Putting it in eqn(i), we get :

=> $$\frac{1}{20} + 12y = \frac{1}{8}$$

=> $$12y = \frac{1}{8} - \frac{1}{20} = \frac{3}{40}$$

=> $$y = \frac{3}{40 \times 12} = \frac{1}{160}$$

Thus, 16 women can complete the work in = $$16 \times \frac{1}{160} = \frac{1}{10}$$

$$\therefore$$ 16 women can complete the work in 10 days.