The ratio of the number of men to the number of women in a 20 member committee is 3:1. How many women must be added to the 20-member committee so as to make the ratio of men to women 3:2?
A. 2 B. 5 C. 7 D. 9
Correct Answer: B
Explanation
20 members in the ratio 3:1 Number of women = \(\frac{1}{4} \times 20\) = 5 Let the number of women to be added = x Total number of members in the committee = 20 + x \(\frac{5 + x}{20 + x} = \frac{2}{5}\) \(5(5 + x) = 2(20 + x)\) \(25 + 5x = 40 + 2x \implies 5x - 2x = 40 - 25\) \(3x = 15 \implies x = 5\)
