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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 & Solution
Correct Answer:
Option
B
Let the number of ladies and gents at the party be 3x and 2x respectively.
Then,
$$\eqalign{ & = \frac{{3x}}{{2x + 20}} = \frac{2}{3} \cr & \Rightarrow 9x = 4x + 40 \cr & \Rightarrow 5x = 40 \cr & \Rightarrow x = 8 \cr} $$
∴ Number of ladies = 3 × 8 = 24
Then,
$$\eqalign{ & = \frac{{3x}}{{2x + 20}} = \frac{2}{3} \cr & \Rightarrow 9x = 4x + 40 \cr & \Rightarrow 5x = 40 \cr & \Rightarrow x = 8 \cr} $$
∴ Number of ladies = 3 × 8 = 24
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