France and Pakistan took part in Youth Games. From France, the ratio of the number of female supporters to the number of male supporters was 3 : 2. From Pakistan, the ratio of the number of female supporters to the number of male supporters was 1 : 2. The total number of supporters from France was ⁵₂₄ the total number of supporters from Pakistan.

1. What was the ratio of the number of female supporters from France to the total number of female supporters from both countries? Express the answer in the simplest form.
2. After another 143 female supporters from both countries joined the games, the percentage of all the male supporters became 54%. How many less male supporters from France than Pakistan were there at first?

France		Pakistan
5 u		24 u
Female supporters	Male supporters	Female supporters	Male supporters
3	2	1x2	2x2
3 u	2 u	8 u	16 u

(a)
Number of female supporters from Pakistan
= ¹₃ x 24 u
= 8 u

Number of male supporters from France
= ²₃ x 24 u
= 16 u

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

Female supporters from France : Total female supporters
3 : 11

(b)

	Female supporters	Male supporters
Before	11x3 = 33%	18x3 = 54%
Change	+ 143
After	46%	54%

Number of female supporters in the end in percent
= 100% - 54%
= 46%

Total number of male supporters at first
= 2 u + 16 u
= 18 u

After another 143 female supporters from both countries joined the games, the percentage of all the male supporters became 54%.

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

18 u = 54%

1 u = 54% ÷ 18 = 3%

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

Number of female supporters from both countries who joined the games
= 46% - 33%
= 13%

13% = 143 

1% = 143 ÷ 13 = 11

Number of less male supporters from France than Pakistan at first
= 16 u - 2 u
= 14 u
= 14 x 3%
= 42%
= 42 x 11
= 462 

Answer(s): (a) 3 : 11; (b) 462