PSLE The number of girls and boys taking part in a test are in the ratio 3 : 8. These students are put into two groups. 80% of the girls and 10% of the boys are in Group K. The rest of the students are in Group L.
- What is the ratio of the number of students in Group L to Group K? Give your answer in the simplest form.
- The number of boys in Group K is more than 90. What is the smallest possible total number of students taking part in the test?
Girls |
Boys |
30 u |
80 u |
Group K |
Group L |
Group K |
Group L |
24 u |
6 u |
8 u |
72 u |
(a)
Girls : Boys
3 : 8
30 : 80
Number of girls in Group K
= 80% x 30 u
=
80100 x 30 u
= 24 u
Number of girls in Group L
= 30 u - 24 u
= 6 u
Number of boys in Group K
= 10% x 80 u
=
10100 x 80 u
= 8 u
Number of boys in Group L
= 80 u - 8 u
= 72 u
Group K : Group L
6 + 72 : 24 + 8
78 : 32
(÷2)39 : 16
(b)
Number of boys in Group K = 8 u
Since the number of boys in Group K is 8 u, it must be multiple of 8.
Number of sets of 8
= 90 ÷ 8
= 11 r 2
Since the number of boys in Group K is more than 90, the number of sets must be 1 more than 11.
1 u = 11 + 1 = 12
Smallest possible number of students
= 30 u + 80 u
= 110 u
= 110 x 12
= 1320
Answer(s): (a) 39 : 16; (b) 1320