PSLE The number of boys and girls taking part in a quiz are in the ratio 2 : 7. These students are put into two groups. 20% of the boys and 50% 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 90. What is the smallest possible total number of students taking part in the quiz?
Boys |
Girls |
20 u |
70 u |
Group L |
Group M |
Group L |
Group M |
4 u |
16 u |
35 u |
35 u |
(a)
Boys : Girls
2 : 7
20 : 70
Number of boys in Group L
= 20% x 20 u
=
20100 x 20 u
= 4 u
Number of boys in Group M
= 20 u - 4 u
= 16 u
Number of girls in Group L
= 50% x 70 u
=
50100 x 70 u
= 35 u
Number of girls in Group M
= 70 u - 35 u
= 35 u
Group L : Group M
16 + 35 : 4 + 35
51 : 39
(÷3)17 : 13
(b)
Number of girls in Group L = 35 u
Since the number of girls in Group L is 35 u, it must be multiple of 35.
Number of sets of 35
= 90 ÷ 35
= 2 r 20
Since the number of girls in Group L is more than 90, the number of sets must be 1 more than 2.
1 u = 2 + 1 = 3
Smallest possible number of students
= 20 u + 70 u
= 90 u
= 90 x 3
= 270
Answer(s): (a) 17 : 13; (b) 270