Korea and Australia took part in Youth Games. From Korea, the ratio of the number of male supporters to the number of female supporters was 2 : 9. From Australia, the ratio of the number of male supporters to the number of female supporters was 1 : 2. The total number of supporters from Korea was ¹¹₂₇ the total number of supporters from Australia.

1. What was the ratio of the number of male supporters from Korea to the total number of male supporters from both countries? Express the answer in the simplest form.
2. After 42 male supporters from both countries left the games, the percentage of all the female supporters became 81%. How many more female supporters from Australia than Korea were there at first?

Korea		Australia
11 u		27 u
Male supporters	Female supporters	Male supporters	Female supporters
2	9	1x3	2x3
2 u	9 u	9 u	18 u

(a)
Number of male supporters from Australia
= ¹₃ x 27 u
= 9 u

Number of female supporters from Korea
= ²₃ x 27 u
= 18 u

Total number of male supporters
= 2 u + 9 u
= 11 u

Male supporters from Korea : Total male supporters
2 : 11

(b)

	Male supporters	Female supporters
Before	11x3 = 33%	27x3 = 81%
Change	- 42
After	19%	81%

Number of male supporters in the end in percent
= 100% - 81%
= 19%

Total number of female supporters at first
= 9 u + 18 u
= 27 u

After 42 male supporters from both countries left the games, the percentage of all the female supporters became 81%.

Since only male supporters left the games, the number of female supporters remains unchanged. Make the number of female supporters the same.

27 u = 81%

1 u = 81% ÷ 27 = 3%

Number of male supporters at first in percent
= 11 x 3%
= 33%

Number of male supporters from both countries who left
= 33% - 19%
= 14%

14% = 42 

1% = 42 ÷ 14 = 3

Number of more female supporters from Australia than Korea at first
= 18 u - 9 u
= 9 u
= 9 x 3%
= 27%
= 27 x 3
= 81 

Answer(s): (a) 2 : 11; (b) 81