Question

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

• A. $36$
• B. $32$
• C. $24$
• D. $16$

Answer 1

The correct option is C $24$

Let the number of ladies and gents in the party be 3x and 2x respectively. Then,
$\frac{3x}{2x+20}=\frac{2}{3}\Rightarrow 9x=4x+40\Rightarrow 5x=40$
$\Rightarrow x=8$
$\therefore$ Number of ladies in the party $=3x=3\times 8=24$