Pakistan and Greece took part in Youth Games. From Pakistan, the ratio of the number of male supporters to the number of female supporters was 3 : 8. From Greece, the ratio of the number of male supporters to the number of female supporters was 1 : 3. The total number of supporters from Pakistan was
1116 the total number of supporters from Greece.
- 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.
- After 88 male supporters from both countries left the games, the percentage of all the female supporters became 80%. How many more female supporters from Greece than Pakistan were there at first?
Pakistan |
Greece |
11 u |
16 u |
Male supporters |
Female supporters |
Male supporters |
Female supporters |
3 |
8 |
1x2 |
3x2 |
3 u |
8 u |
4 u |
12 u |
(a)
Number of male supporters from Greece
=
14 x 16 u
= 4 u
Number of female supporters from Pakistan
=
34 x 16 u
= 12 u
Total number of male supporters
= 3 u + 4 u
= 7 u
Male supporters from Pakistan : Total male supporters
3 : 7
(b)
|
Male supporters |
Female supporters |
Before |
7x4 = 28% |
20x4 = 80% |
Change |
- 88 |
|
After |
20% |
80% |
Number of male supporters in the end in percent
= 100% - 80%
= 20%
Total number of female supporters at first
= 8 u + 12 u
= 20 u
After 88 male supporters from both countries left the games, the percentage of all the female supporters became 80%.
Since only male supporters left the games, the number of female supporters remains unchanged. Make the number of female supporters the same.
20 u = 80%
1 u = 80% ÷ 20 =
4%Number of male supporters at first in percent
= 7 x 4%
= 28%
Number of male supporters from both countries who left
= 28% - 20%
= 8%
8% = 88
1% = 88 ÷ 8 =
11Number of more female supporters from Greece than Pakistan at first
= 12 u - 8 u
= 4 u
= 4 x 4%
= 16%
= 16 x 11
= 176
Answer(s): (a) 3 : 7; (b) 176