Initially, there are 32 people in a room, with a ratio of 5 men for every 3 women. 18 men leave, and the number of women in the room then diminishes, so that the number of women in the room is equal to twice the number of men in the room. In order to have a 2 : 1 ratio of men to women in the room, how many more men must be added?
The initial ratio has 8 total parts (5 men and 3 women) and a total of 32 people; each part must be equal to 4 people, giving us actual numbers of 20 mean and 12 women.
18 men leave, leaving us with 2 men. We also know that we now have twice as many women as men (2*2=4), so 8 women must leave as well.
A 2:1 ratio of men to women means that we need twice as many men as women. We have 4 women; 4*2=8 men, so we must add 6 men.
