Japan and Fiji took part in Youth Games. From Japan, the ratio of the number of male supporters to the number of female supporters was 4 : 9. From Fiji, the ratio of the number of male supporters to the number of female supporters was 1 : 2. The total number of supporters from Japan was ¹³₂₇ the total number of supporters from Fiji.

1. What was the ratio of the number of male supporters from Japan to the total number of male supporters from both countries? Express the answer in the simplest form.
2. After 140 male supporters from both countries left the games, the percentage of all the female supporters became 81%. How many more female supporters from Fiji than Japan were there at first?

Japan		Fiji
13 u		27 u
Male supporters	Female supporters	Male supporters	Female supporters
4	9	1x3	2x3
4 u	9 u	9 u	18 u

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

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

Total number of male supporters
= 4 u + 9 u
= 13 u

Male supporters from Japan : Total male supporters
4 : 13

(b)

	Male supporters	Female supporters
Before	13x3 = 39%	27x3 = 81%
Change	- 140
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 140 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
= 13 x 3%
= 39%

Number of male supporters from both countries who left
= 39% - 19%
= 20%

20% = 140 

1% = 140 ÷ 20 = 7

Number of more female supporters from Fiji than Japan at first
= 18 u - 9 u
= 9 u
= 9 x 3%
= 27%
= 27 x 7
= 189 

Answer(s): (a) 4 : 13; (b) 189