China and India took part in Youth Games. From China, the ratio of the number of male supporters to the number of female supporters was 3 : 2. From India, the ratio of the number of male supporters to the number of female supporters was 2 : 7. The total number of supporters from China was ⁵₁₈ the total number of supporters from India.

1. What was the ratio of the number of male supporters from China to the total number of male supporters from both countries? Express the answer in the simplest form.
2. After another 378 male supporters from both countries joined the games, the percentage of all the female supporters became 32%. How many less female supporters from China than India were there at first?

China		India
5 u		18 u
Male supporters	Female supporters	Male supporters	Female supporters
3	2	2x2	7x2
3 u	2 u	4 u	14 u

(a)
Number of male supporters from India
= ²₉ x 18 u
= 4 u

Number of female supporters from China
= ⁷₉ x 18 u
= 14 u

Total number of male supporters
= 3 u + 4 u
= 7 u

Male supporters from China : Total male supporters
3 : 7

(b)

	Male supporters	Female supporters
Before	7x2 = 14%	16x2 = 32%
Change	+ 378
After	68%	32%

Number of male supporters in the end in percent
= 100% - 32%
= 68%

Total number of female supporters at first
= 2 u + 14 u
= 16 u

After another 378 male supporters from both countries joined the games, the percentage of all the female supporters became 32%.

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

16 u = 32%

1 u = 32% ÷ 16 = 2%

Number of male supporters at first in percent
= 7 x 2%
= 14%

Number of male supporters from both countries who joined the games
= 68% - 14%
= 54%

54% = 378 

1% = 378 ÷ 54 = 7

Number of less female supporters from China than India at first
= 14 u - 2 u
= 12 u
= 12 x 2%
= 24%
= 24 x 7
= 168 

Answer(s): (a) 3 : 7; (b) 168