PSLE At first, the ratio of the number of girls to the number of boys in a school was 3 : 2. After 30 girls and 30 boys left the school, the ratio became 9 : 4.
- Did the percentage of pupils who were boys increase (1), decrease (2) or remain the same (3)? Give your answer in number. (Eg Increase = 1)
- In the end, how many boys were there in the school?
|
Girls |
Boys |
Difference |
Total |
Before |
3x5 = 15 u
|
2x5 = 10 u
|
1x5 = 5 u
|
15 u + 10 u = 25 u |
Change |
- 30 |
- 30 |
|
|
After |
9x1 = 9 u |
4x1 = 4 u |
5x1 = 5 u |
9 u + 4 u = 13 u |
(a)
30 girls and 30 boys left the school. There was equal number of girls and boys who left the school.
Since the decrease in number of pupils in both groups is the same, the difference between the number of girls and boys remains unchanged.
We make the difference between the number of girls and boys at first and in the end the same.
LCM of 1 and 5 = 5 u
Percent of pupils who were boys at first
=
1025 x 100%
≈ 40% (Round off to whole number.)
Percent of pupils who are boys in the end
=
413 x 100%
≈ 31% (Round off to whole number.)
Percent of pupils who were boys
decreased from 40% to 31%. (2)
(b)
Decrease in the number of girls
= 9 u - 15 u
= 6 u
6 u = 30
1 u = 30 ÷ 6 = 5
Number of boys in the end
= 4 u
= 4 x 5
= 20
Answer(s): (a) 2; (b) 20