China and Egypt took part in Youth Games. From China, the ratio of the number of female supporters to the number of male supporters was 3 : 2. From Egypt, the ratio of the number of female supporters to the number of male supporters was 4 : 5. The total number of supporters from China was ⁵₁₈ the total number of supporters from Egypt.

1. What was the ratio of the number of female supporters from China to the total number of female supporters from both countries? Express the answer in the simplest form.
2. After another 40 female supporters from both countries joined the games, the percentage of all the male supporters became 48%. How many less male supporters from China than Egypt were there at first?

China		Egypt
5 u		18 u
Female supporters	Male supporters	Female supporters	Male supporters
3	2	4x2	5x2
3 u	2 u	8 u	10 u

(a)
Number of female supporters from Egypt
= ⁴₉ x 18 u
= 8 u

Number of male supporters from China
= ⁵₉ x 18 u
= 10 u

Total number of female supporters
= 3 u + 8 u
= 11 u

Female supporters from China : Total female supporters
3 : 11

(b)

	Female supporters	Male supporters
Before	11x4 = 44%	12x4 = 48%
Change	+ 40
After	52%	48%

Number of female supporters in the end in percent
= 100% - 48%
= 52%

Total number of male supporters at first
= 2 u + 10 u
= 12 u

After another 40 female supporters from both countries joined the games, the percentage of all the male supporters became 48%.

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

12 u = 48%

1 u = 48% ÷ 12 = 4%

Number of female supporters at first in percent
= 11 x 4%
= 44%

Number of female supporters from both countries who joined the games
= 52% - 44%
= 8%

8% = 40 

1% = 40 ÷ 8 = 5

Number of less male supporters from China than Egypt at first
= 10 u - 2 u
= 8 u
= 8 x 4%
= 32%
= 32 x 5
= 160 

Answer(s): (a) 3 : 11; (b) 160