Question

In a meeting the ratio of men to women was 1:2 but after 2 men and 2 women left, the ratio becomes 1:3. What was the total no. of people attending the meeting?

Answer 1

The ratio of the number of women to the number of men to the number of children in a room is 5:2:7, respectively. What is the total number of people in the room?

(1) The total number of women and children in the room is 12.
(2) There are fewer than 4 men in the room.

Spoiler: OA


Last edited by Bunuel on 24 Sep 2013, 07:40, edited 1 time in total.

Say total number of people are = 70x
So Women = 70x*5/14 = 25x
Children = 7*70x/14 = 35x
Men = 2*70x/14 = 10x

Statement 1:
Tells us 25x + 35x = 60x = 12, so total number of people = 70/5 = 14. So you know total number of people. Question is answered.

Statement 2:
Tells us there are fewer than 4 men in room. So it can be 1, 2, or 3. 
If Men = 1, then women = 5/2 *1 = 2.5 So Not Possible
If Men = 2, then Women = 5/2 * 2 = 5, and Children = 7/2 * 2 = 7
If Men = 3, then Women = 5/2 * 3 = 7.5 So Not Possible.
From this statement also we know what the total number of people is. So this also answers the question.