Brunei and Brazil took part in Youth Games. From Brunei, the ratio of the number of female supporters to the number of male supporters was 1 : 12. From Brazil, the ratio of the number of female supporters to the number of male supporters was 1 : 6. The total number of supporters from Brunei was ¹³₂₁ the total number of supporters from Brazil.

1. What was the ratio of the number of female supporters from Brunei to the total number of female supporters from both countries? Express the answer in the simplest form.
2. After 6 female supporters from both countries left the games, the percentage of all the male supporters became 90%. How many more male supporters from Brazil than Brunei were there at first?

Brunei		Brazil
13 u		21 u
Female supporters	Male supporters	Female supporters	Male supporters
1	12	1x3	6x3
1 u	12 u	3 u	18 u

(a)
Number of female supporters from Brazil
= ¹₇ x 21 u
= 3 u

Number of male supporters from Brunei
= ⁶₇ x 21 u
= 18 u

Total number of female supporters
= 1 u + 3 u
= 4 u

Female supporters from Brunei : Total female supporters
1 : 4

(b)

	Female supporters	Male supporters
Before	4x3 = 12%	30x3 = 90%
Change	- 6
After	10%	90%

Number of female supporters in the end in percent
= 100% - 90%
= 10%

Total number of male supporters at first
= 12 u + 18 u
= 30 u

After 6 female supporters from both countries left the games, the percentage of all the male supporters became 90%.

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

30 u = 90%

1 u = 90% ÷ 30 = 3%

Number of female supporters at first in percent
= 4 x 3%
= 12%

Number of female supporters from both countries who left
= 12% - 10%
= 2%

2% = 6 

1% = 6 ÷ 2 = 3

Number of more male supporters from Brazil than Brunei at first
= 18 u - 12 u
= 6 u
= 6 x 3%
= 18%
= 18 x 3
= 54 

Answer(s): (a) 1 : 4; (b) 54