Womens

let $x$ be the number of women to leave the room

$\dfrac{40-x}{100-x}=0.2$ $\implies$ $40-x=20-0.2x$ $\implies$ $20=0.8x$ $\implies$ $\color{#D61F06}\boxed{x=25}$

Since the original number of people is 100, 40% of women means that there are 40 women.

Now

Let the amount of women who left be X.

Then ( 40 - X ) / ( 100 - X ) = 20

40 - 20 = X - X/ 5

20 = ( 5X - X) / 5

100 = 4X / 5

X = 25 ,

$40$ % of $100$ is $40$

Let $w =$ Amount of woman leaving

We're looking for $20$ % of the new amount of people which will be $100 - w$ . However we also need the new amount of women which is $40 - w$ .

This means that

$40 - w = \frac {1}{5} \cdot (100 - w)$

Re-arranging this gives us an equation for $w$

$w = -\frac {1}{5} \cdot (100 - w) + 40$

Expanding and simplifying it gives us

$w = \frac {w}{5} + 20$

We're almost there, now we re-arrange it again to get

$\frac {4w}{5} = 20$

Simplifying this gives us a value for $w$

$w = 25$

Let the number of women who leave the room be x.

The new number of women will be 40-x and the number of people in the room will be 100-x.

According to the question:

(40-x) = (20/100)(100-x)

5(40-x) = 200-5x = 100-x

100 = 4x

x = 25

Let the number of women who leave the room is x, so (40-x)/(100-x) = 1/5, the x=25.