The committee

Let $m$ and $w$ be the number of men and woman, respectively, in the $20$ member committee. The ratio of the number of men to the number of women is $3:1$ , so the total is $1+3=4$ . So

$m=\dfrac{3}{4}(20)=15$

$w=\dfrac{1}{4}(20)=5$

Let $x$ be the number of woman to be added to make a new ratio of $3:2$ . We have

$\dfrac{15}{5+x}=\dfrac{3}{2}$

$30=15+3x$

$3x=15$

$\boxed{x=5}$

3+1=4, 3+2=5
(20/4) * 5 = 25....total members in new committee
5 * 3 = 15(Men)
5 * 2 = 10(Women)
10-5 = 5......req. to add 5 women