India and Chile took part in Youth Games. From India, the ratio of the number of male supporters to the number of female supporters was 1 : 10. From Chile, the ratio of the number of male supporters to the number of female supporters was 1 : 3. The total number of supporters from India was ¹¹₂₄ the total number of supporters from Chile.

1. What was the ratio of the number of male supporters from India to the total number of male supporters from both countries? Express the answer in the simplest form.
2. After 20 male supporters from both countries left the games, the percentage of all the female supporters became 84%. How many more female supporters from Chile than India were there at first?

India		Chile
11 u		24 u
Male supporters	Female supporters	Male supporters	Female supporters
1	10	1x2	3x2
1 u	10 u	6 u	18 u

(a)
Number of male supporters from Chile
= ¹₄ x 24 u
= 6 u

Number of female supporters from India
= ³₄ x 24 u
= 18 u

Total number of male supporters
= 1 u + 6 u
= 7 u

Male supporters from India : Total male supporters
1 : 7

(b)

	Male supporters	Female supporters
Before	7x3 = 21%	28x3 = 84%
Change	- 20
After	16%	84%

Number of male supporters in the end in percent
= 100% - 84%
= 16%

Total number of female supporters at first
= 10 u + 18 u
= 28 u

After 20 male supporters from both countries left the games, the percentage of all the female supporters became 84%.

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

28 u = 84%

1 u = 84% ÷ 28 = 3%

Number of male supporters at first in percent
= 7 x 3%
= 21%

Number of male supporters from both countries who left
= 21% - 16%
= 5%

5% = 20 

1% = 20 ÷ 5 = 4

Number of more female supporters from Chile than India at first
= 18 u - 10 u
= 8 u
= 8 x 3%
= 24%
= 24 x 4
= 96 

Answer(s): (a) 1 : 7; (b) 96