PSLE At first, the ratio of the number of boys to the number of girls in a school was 9 : 4. After 51 boys and 51 girls joined the school, the ratio became 7 : 5.
- Did the percentage of pupils 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 boys were there in the school?
|
Boys |
Girls |
Difference |
Total |
Before |
9x2 = 18 u
|
4x2 = 8 u
|
5x2 = 10 u
|
18 u + 8 u = 26 u |
Change |
+ 51 |
+ 51 |
|
|
After |
7x5 = 35 u |
5x5 = 25 u |
2x5 = 10 u |
35 u + 25 u = 60 u |
(a)
51 boys and 51 girls joined the school. There was equal number of boys and girls who joined the school.
Since the increase in number of pupils in both groups is the same, the difference between the number of boys and girls remains unchanged.
We make the difference between the number of boys and girls at first and in the end the same.
LCM of 5 and 2 = 10 u
Percent of pupils who were girls at first
=
826 x 100%
≈ 31% (Round off to whole number.)
Percent of pupils who are girls in the end
=
2560 x 100%
≈ 42% (Round off to whole number.)
Percent of pupils who were girls
increased from 31% to 42%. (1)
(b)
Increase in the number of boys
= 35 u - 18 u
= 17 u
17 u = 51
1 u = 51 ÷ 17 = 3
Number of boys in the end
= 35 u
= 35 x 3
= 105
Answer(s): (a) 1; (b) 105