PSLE
The number of boys and girls taking part in a quiz are in the ratio 3 : 2. These students are put into two groups. 60% of the boys and 20% of the girls are in Group S. The rest of the students are in Group T.

1. What is the ratio of the number of students in Group T to Group S? Give your answer in the simplest form.
2. The number of girls in Group S is more than 50. What is the smallest possible total number of students taking part in the quiz?

Boys		Girls
30 u		20 u
Group S	Group T	Group S	Group T
18 u	12 u	4 u	16 u

(a)
Boys : Girls
3 : 2
30 : 20

Number of boys in Group S
= 60% x 30 u
= ⁶⁰₁₀₀ x 30 u
= 18 u

Number of boys in Group T
= 30 u - 18 u
= 12 u

Number of girls in Group S
= 20% x 20 u
= ²⁰₁₀₀ x 20 u
= 4 u

Number of girls in Group T
= 20 u - 4 u
= 16 u

Group S : Group T
12 + 16 : 18 + 4 
28 : 22 _(÷2)
14 : 11

(b)
Number of girls in Group S = 4 u

Since the number of girls in Group S is 4 u, it must be multiple of 4.

Number of sets of 4
= 50 ÷ 4
= 12 r 2

Since the number of girls in Group S is more than 50, the number of sets must be 1 more than 12.

1 u = 12 + 1 = 13

Smallest possible number of students
= 30 u + 20 u
= 50 u
= 50 x 13
= 650

Answer(s): (a) 14 : 11; (b) 650