Some persons can do a piece of work in 84 days. Two times the number of such persons will do half of the same work in how many days?

$$\frac{M_1\times\ D_1}{W_1}\ =\ \frac{M_2\times\ D_2}{W_2}$$

In first case, let's assume the number of persons are $$M_1$$ and work is $$W_1$$.

In the second case, let's assume the number of persons are $$M_2$$ and work is $$\frac{W_1}{2}$$.

So $$M_2 = 2M_1$$ and $$W_2 = \frac{W_1}{2}$$

Here $$D_2$$ is the required number of days in the second case.

$$\frac{M_1\times\ 84}{W_1}\ =\ \frac{2M_1\times\ D_2}{\frac{W_1}{2}}$$

$$84\ =2\times\ 2D_2$$

$$84\ =4D_2$$

$$D_2 = 21$$ days