Pakistan and Australia took part in Youth Games. From Pakistan, the ratio of the number of male supporters to the number of female supporters was 1 : 12. From Australia, the ratio of the number of male supporters to the number of female supporters was 1 : 2. The total number of supporters from Pakistan was ¹³₂₇ the total number of supporters from Australia.

1. What was the ratio of the number of male supporters from Pakistan to the total number of male supporters from both countries? Express the answer in the simplest form.
2. After 60 male supporters from both countries left the games, the percentage of all the female supporters became 90%. How many more female supporters from Australia than Pakistan were there at first?

Pakistan		Australia
13 u		27 u
Male supporters	Female supporters	Male supporters	Female supporters
1	12	1x3	2x3
1 u	12 u	9 u	18 u

(a)
Number of male supporters from Australia
= ¹₃ x 27 u
= 9 u

Number of female supporters from Pakistan
= ²₃ x 27 u
= 18 u

Total number of male supporters
= 1 u + 9 u
= 10 u

Male supporters from Pakistan : Total male supporters
1 : 10

(b)

	Male supporters	Female supporters
Before	10x3 = 30%	30x3 = 90%
Change	- 60
After	10%	90%

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

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

After 60 male supporters from both countries left the games, the percentage of all the female supporters became 90%.

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

30 u = 90%

1 u = 90% ÷ 30 = 3%

Number of male supporters at first in percent
= 10 x 3%
= 30%

Number of male supporters from both countries who left
= 30% - 10%
= 20%

20% = 60 

1% = 60 ÷ 20 = 3

Number of more female supporters from Australia than Pakistan at first
= 18 u - 12 u
= 6 u
= 6 x 3%
= 18%
= 18 x 3
= 54 

Answer(s): (a) 1 : 10; (b) 54