The ratio of men to women in a 20-member committee is 3:1. How many women must be added to the committee to make the ratio of men to women 3:2?

Analyze the question: We have a committee of 20 members with men to women in the ratio 3:1. We add some women so the new ratio of men to women becomes 3:2. We need to find how many women are added.

Concept: When women are added, the number of men stays the same. Only the number of women changes.

Solution:

Step 1: Find the number of men and women now. Total parts = 3 + 1 = 4

• Men = (3/4) × 20 = 15
• Women = (1/4) × 20 = 5

Step 2: Let x be the number of women added. New ratio: 15 : (5 + x) = 3 : 2

Step 3: Cross-multiply. 3(5 + x) = 15 × 2 15 + 3x = 30 3x = 15 x = 5

Step 4: Check. Men = 15, women = 5 + 5 = 10. Ratio 15:10 = 3:2 ✓

Answer: 5 women must be added, which is option B.

Tip: In "add to one group" ratio problems, find the group that does not change (here, the men). Use it as your fixed anchor. Convert the new ratio so the fixed group matches: 3:2 means 15 men goes with 10 women, so 10 − 5 = 5 added.