Catholic High School 2010 PSLE Math Prelim Paper 2 Q18

At a conference made up of speakers and participants, there were 20% more men than women. The ratio of male speakers to female speakers was 8:5. There was an equal number of male and female participants.
a) Find the ratio of male speakers to male participants at the conference.
b) Halfway, 40 male participants left the conference and another 60 female participants joined the conference. In the end, there were 3/4 as many male participants as female participants remaining behind. How many speakers were there at the conference?

Solution

Male ----- 120%
Female ----- 100%

Speakers
Male : Female
8 (parts) : 5 (parts)

Participants
Male : Female
1 (unit) : 1 (unit)

Men ----- 8 parts + 1 unit
Women ----- 5 parts + 1 unit

But since there are 20% more women than men,
Women ----- 5 parts x 120% + 1 unit x 120%
= 6 parts + 1.2 units

Men ----- Women
8 parts + 1 unit ----- 6 parts + 1.2 units
8 parts - 6 parts ----- 1.2 units - 1 unit
2 parts ----- 0.2 unit
1 part ----- 0.1 unit
10 parts ----- 1 unit
or
1 unit ----- 10 parts


(a)
Male Speakers ----- 8 parts
Male Participants ----- 1 unit or 10 parts

Male Speakers : Male Participants
8 : 10
4 : 5

Answer: 4 : 5

(b)
Speakers
Male : Female
8 (parts) : 5 (parts) -- (altogether 13 parts)

Participants
Male : Female
1 (unit) : 1 (unit)
10 (parts) : 10 (parts) -- (before)
- 40 : + 60 -- (40 males left; 60 females joined)
3 (units) : 4 (units) -- (3/4 as many male as females in the end)

(Male) 3 units ----- 10 parts - 40
(Female) 4 units ----- 10 parts + 60

(Female) - (Male)
4 units - 3 units ----- 10 parts + 60 - 10 parts - (-40)
1 unit ----- 60 + 40
1 unit ----- 100

(Male after)
3 units ---- 3 x 100 = 300

(Male before)
10 parts ---- 300 + 40 (need to add the 40 who left)
10 parts ----- 340
1 part ---- 34

All speakers
13 parts ---- 13 x 34 = 442

Answer: 442 speakers

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