PSLE The number of boys and girls taking part in a contest are in the ratio 7 : 6. These students are put into two groups. 60% of the boys and 20% of the girls are in Group L. The rest of the students are in Group M.
- What is the ratio of the number of students in Group M to Group L? Give your answer in the simplest form.
- The number of girls in Group L is more than 80. What is the smallest possible total number of students taking part in the contest?
Boys |
Girls |
70 u |
60 u |
Group L |
Group M |
Group L |
Group M |
42 u |
28 u |
12 u |
48 u |
(a)
Boys : Girls
7 : 6
70 : 60
Number of boys in Group L
= 60% x 70 u
=
60100 x 70 u
= 42 u
Number of boys in Group M
= 70 u - 42 u
= 28 u
Number of girls in Group L
= 20% x 60 u
=
20100 x 60 u
= 12 u
Number of girls in Group M
= 60 u - 12 u
= 48 u
Group L : Group M
28 + 48 : 42 + 12
76 : 54
(÷2)38 : 27
(b)
Number of girls in Group L = 12 u
Since the number of girls in Group L is 12 u, it must be multiple of 12.
Number of sets of 12
= 80 ÷ 12
= 6 r 8
Since the number of girls in Group L is more than 80, the number of sets must be 1 more than 6.
1 u = 6 + 1 = 7
Smallest possible number of students
= 70 u + 60 u
= 130 u
= 130 x 7
= 910
Answer(s): (a) 38 : 27; (b) 910