PSLE The number of boys and girls taking part in a contest are in the ratio 7 : 8. These students are put into two groups. 70% of the boys and 20% of the girls 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 girls in Group K is more than 60. What is the smallest possible total number of students taking part in the contest?
Boys |
Girls |
70 u |
80 u |
Group K |
Group L |
Group K |
Group L |
49 u |
21 u |
16 u |
64 u |
(a)
Boys : Girls
7 : 8
70 : 80
Number of boys in Group K
= 70% x 70 u
=
70100 x 70 u
= 49 u
Number of boys in Group L
= 70 u - 49 u
= 21 u
Number of girls in Group K
= 20% x 80 u
=
20100 x 80 u
= 16 u
Number of girls in Group L
= 80 u - 16 u
= 64 u
Group K : Group L
21 + 64 : 49 + 16
85 : 65
(÷5)17 : 13
(b)
Number of girls in Group K = 16 u
Since the number of girls in Group K is 16 u, it must be multiple of 16.
Number of sets of 16
= 60 ÷ 16
= 3 r 12
Since the number of girls in Group K is more than 60, the number of sets must be 1 more than 3.
1 u = 3 + 1 = 4
Smallest possible number of students
= 70 u + 80 u
= 150 u
= 150 x 4
= 600
Answer(s): (a) 17 : 13; (b) 600