India and Japan took part in Youth Games. From India, the ratio of the number of male supporters to the number of female supporters was 4 : 9. From Japan, the ratio of the number of male supporters to the number of female supporters was 3 : 4. The total number of supporters from India was ¹³₂₁ the total number of supporters from Japan.

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 6 male supporters from both countries left the games, the percentage of all the female supporters became 63%. How many more female supporters from Japan than India were there at first?

India		Japan
13 u		21 u
Male supporters	Female supporters	Male supporters	Female supporters
4	9	3x3	4x3
4 u	9 u	9 u	12 u

(a)
Number of male supporters from Japan
= ³₇ x 21 u
= 9 u

Number of female supporters from India
= ⁴₇ x 21 u
= 12 u

Total number of male supporters
= 4 u + 9 u
= 13 u

Male supporters from India : Total male supporters
4 : 13

(b)

	Male supporters	Female supporters
Before	13x3 = 39%	21x3 = 63%
Change	- 6
After	37%	63%

Number of male supporters in the end in percent
= 100% - 63%
= 37%

Total number of female supporters at first
= 9 u + 12 u
= 21 u

After 6 male supporters from both countries left the games, the percentage of all the female supporters became 63%.

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

21 u = 63%

1 u = 63% ÷ 21 = 3%

Number of male supporters at first in percent
= 13 x 3%
= 39%

Number of male supporters from both countries who left
= 39% - 37%
= 2%

2% = 6 

1% = 6 ÷ 2 = 3

Number of more female supporters from Japan than India at first
= 12 u - 9 u
= 3 u
= 3 x 3%
= 9%
= 9 x 3
= 27 

Answer(s): (a) 4 : 13; (b) 27