Japan and Denmark took part in Youth Games. From Japan, the ratio of the number of male supporters to the number of female supporters was 1 : 6. From Denmark, the ratio of the number of male supporters to the number of female supporters was 1 : 4. The total number of supporters from Japan was ⁷₂₀ the total number of supporters from Denmark.

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 40 male supporters from both countries left the games, the percentage of all the female supporters became 88%. How many more female supporters from Denmark than Japan were there at first?

Japan		Denmark
7 u		20 u
Male supporters	Female supporters	Male supporters	Female supporters
1	6	1x2	4x2
1 u	6 u	4 u	16 u

(a)
Number of male supporters from Denmark
= ¹₅ x 20 u
= 4 u

Number of female supporters from Japan
= ⁴₅ x 20 u
= 16 u

Total number of male supporters
= 1 u + 4 u
= 5 u

Male supporters from Japan : Total male supporters
1 : 5

(b)

	Male supporters	Female supporters
Before	5x4 = 20%	22x4 = 88%
Change	- 40
After	12%	88%

Number of male supporters in the end in percent
= 100% - 88%
= 12%

Total number of female supporters at first
= 6 u + 16 u
= 22 u

After 40 male supporters from both countries left the games, the percentage of all the female supporters became 88%.

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

22 u = 88%

1 u = 88% ÷ 22 = 4%

Number of male supporters at first in percent
= 5 x 4%
= 20%

Number of male supporters from both countries who left
= 20% - 12%
= 8%

8% = 40 

1% = 40 ÷ 8 = 5

Number of more female supporters from Denmark than Japan at first
= 16 u - 6 u
= 10 u
= 10 x 4%
= 40%
= 40 x 5
= 200 

Answer(s): (a) 1 : 5; (b) 200