PSLE At first, the ratio of the number of boys to the number of girls in a school was 1 : 6. After 32 girls and 32 boys joined the school, the ratio became 1 : 2.
- Did the percentage of students who were girls increase (1), decrease (2) or remain the same (3)? Give your answer in number. (Eg Increase = 1)
- In the end, how many students were there in the school?
|
Boys |
Girls |
Difference |
Total |
Before |
1x1 = 1 u
|
6x1 = 6 u |
5x1 = 5 u
|
1 u + 6 u = 7 u |
Change |
+ 32 |
+ 32 |
|
|
After |
1x5 = 5 u |
2x5 = 10 u |
1x5 = 5 u |
5 u + 10 u = 15 u |
(a)
32 girls and 32 boys joined the school. There was equal number of girls and boys who joined the school.
Since the increase in number of students 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 5 and 1 = 5 u
Percent of students who were girls at first
=
67 x 100%
≈ 86% (Round off to whole number.)
Percent of students who are boys in the end
=
1015 x 100%
≈ 67% (Round off to whole number.)
Percent of students who were girls
decreased from 86% to 67%. (2)
(b)
Increase in the number of girls
= 10 u - 6 u
= 4 u
4 u = 32
1 u = 32 ÷ 4 = 8
Number of students in the end
= 15 u
= 15 x 8
= 120
Answer(s): (a) 2; (b) 120