Russia and India took part in Youth Games. From Russia, the ratio of the number of female supporters to the number of male supporters was 4 : 1. From India, the ratio of the number of female supporters to the number of male supporters was 1 : 2. The total number of supporters from Russia was ⁵₂₇ the total number of supporters from India.

1. What was the ratio of the number of female supporters from Russia to the total number of female supporters from both countries? Express the answer in the simplest form.
2. After 224 female supporters from both countries left the games, the percentage of all the male supporters became 76%. How many more male supporters from India than Russia were there at first?

Russia		India
5 u		27 u
Female supporters	Male supporters	Female supporters	Male supporters
4	1	1x3	2x3
4 u	1 u	9 u	18 u

(a)
Number of female supporters from India
= ¹₃ x 27 u
= 9 u

Number of male supporters from Russia
= ²₃ x 27 u
= 18 u

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

Female supporters from Russia : Total female supporters
4 : 13

(b)

	Female supporters	Male supporters
Before	13x4 = 52%	19x4 = 76%
Change	- 224
After	24%	76%

Number of female supporters in the end in percent
= 100% - 76%
= 24%

Total number of male supporters at first
= 1 u + 18 u
= 19 u

After 224 female supporters from both countries left the games, the percentage of all the male supporters became 76%.

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

19 u = 76%

1 u = 76% ÷ 19 = 4%

Number of female supporters at first in percent
= 13 x 4%
= 52%

Number of female supporters from both countries who left
= 52% - 24%
= 28%

28% = 224 

1% = 224 ÷ 28 = 8

Number of more male supporters from India than Russia at first
= 18 u - 1 u
= 17 u
= 17 x 4%
= 68%
= 68 x 8
= 544 

Answer(s): (a) 4 : 13; (b) 544