At a conference made up of speakers and participants, there were 20% more men than women. The ratio of the male speakers to female speakers was 5 : 2. There was an equal number of male and female participants.
- Find the ratio of male speakers to male participants at the conference at first.
- Halfway, 21 male participants left the conference and another 3 female participants joined the conference. In the end, there were 45 as many male participants as female participants remaining behind. How many speakers were there at the conference?
Men |
Women |
6 groups |
5 groups |
Speakers |
Participants |
Speakers |
Participants |
5 u |
1 p |
2 u |
1 p |
(a)
Number of more men than women
= 100% + 20%
= 120%
120% =
120100 =
65 Men : Women
6 : 5
5 u + 1 p = 6 groups --- (1)
2 u + 1 p = 5 groups --- (2)
(1) - (2)
6 groups - 5 groups = (5 u + 1 p) - (2 u + 1 p)
1 group = 5 u - 2 u
1 group = 3 u
Number of men
= 6 groups
= 6 x 3 u
= 18 u
Number of male participants
= 18 u - 5 u
= 13 u
Male speakers : Male participants
5 : 13
|
Male Participants |
Female Participants |
Before |
13 u |
13 u |
Change |
- 21 |
+ 3 |
After |
4 boxes |
5 boxes |
4 boxes + 21 = 13 u --- (3)
5 boxes - 3 = 13 u --- (4)
(4) = (3)
5 boxes - 3 = 4 boxes + 21
5 boxes - 4 boxes = 21 + 3
1 box = 24
Number of male participants in the end
= 4 boxes
= 4 x 24
= 96
Number of male participants at first
= 96 + 21
= 117
13 u = 117
1 u = 117 ÷ 13 = 9
Number of speakers
= 5 u + 2 u
= 7 u
= 7 x 9
= 63
Answer(s): (a) 5 : 13; (b) 63