In a religious gathering, the ratio of number of ladies to that of gents was 3 ∶ 2 When 20 more gents joined, the ratio was reversed. The number of ladies was

Let the initial number of ladies and gents be $3x$ and $2x$ respectively, based on the given ratio $3:2$.According to the question, $20$ more gents join the gathering, so the number of gents becomes $(2x+20)$. The number of ladies stays the same ($3x$).The new ratio of ladies to gents reverses to become $2:3$:
$$\frac{3x}{2x+20}=\frac{2}{3}$$
Cross-multiplying to solve for $x$:
$$3(3x)=2(2x+20)$$
$$9x=4x+40$$
$$5x=40⟹x=8$$
Now, find the total number of ladies:
$$\text{Number of ladies}=3x=3(8)=24$$