The ratio of the number of ladies to that of gents at a party was 3 : 2. When 20 more gents joined the party, the ratio was reversed. The number of ladies present at the party was -

Answer: Option B

Let the number of ladies and gents at the party be 3x and 2x respectively.
Then,
$$\begin{array}{rl}& =\frac{3x}{2x+20}=\frac{2}{3}\\ & \Rightarrow 9x=4x+40\\ & \Rightarrow 5x=40\\ & \Rightarrow x=8\end{array}$$
∴ Number of ladies = 3 × 8 = 24