PSLE The number of boys and girls taking part in a quiz are in the ratio 3 : 7. These students are put into two groups. 80% of the boys and 20% of the girls are in Group S. The rest of the students are in Group T.
- What is the ratio of the number of students in Group T to Group S? Give your answer in the simplest form.
- The number of girls in Group S is more than 90. What is the smallest possible total number of students taking part in the quiz?
Boys |
Girls |
30 u |
70 u |
Group S |
Group T |
Group S |
Group T |
24 u |
6 u |
14 u |
56 u |
(a)
Boys : Girls
3 : 7
30 : 70
Number of boys in Group S
= 80% x 30 u
=
80100 x 30 u
= 24 u
Number of boys in Group T
= 30 u - 24 u
= 6 u
Number of girls in Group S
= 20% x 70 u
=
20100 x 70 u
= 14 u
Number of girls in Group T
= 70 u - 14 u
= 56 u
Group S : Group T
6 + 56 : 24 + 14
62 : 38
(÷2)31 : 19
(b)
Number of girls in Group S = 14 u
Since the number of girls in Group S is 14 u, it must be multiple of 14.
Number of sets of 14
= 90 ÷ 14
= 6 r 6
Since the number of girls in Group S is more than 90, the number of sets must be 1 more than 6.
1 u = 6 + 1 = 7
Smallest possible number of students
= 30 u + 70 u
= 100 u
= 100 x 7
= 700
Answer(s): (a) 31 : 19; (b) 700