In a religious gathering, the ratio of number of ladies to that of gents was…
20172021
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
- A.
36
- B.
40
- C.
16
- D.
24
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Correct answer: D
When a ratio between two quantities changes because a fixed amount is added to only one of them, express both original quantities as multiples of a common variable using the given ratio, then write a new equation from the changed ratio and solve for that variable.
Let the initial number of ladies be 3x and gents be 2x, since the ratio of ladies to gents was 3:2.
After 20 more gents joined, the number of gents becomes 2x + 20, while the ladies remain 3x.
The ratio was reversed, so the new ratio of ladies to gents is 2:3, giving the equation 3x / (2x + 20) = 2/3.
Cross-multiplying gives 3x × 3 = 2 × (2x + 20), i.e., 9x = 4x + 40, so 5x = 40 and x = 8.
The number of ladies is 3x = 3 × 8 = 24.
Checking: gents before joining = 2x = 16, and after 20 more join, gents = 36. The ratio of ladies to gents is 24:36 = 2:3, which matches the reversed ratio, confirming the answer.