PSLE
The number of boys and girls taking part in a contest are in the ratio 7 : 2. These students are put into two groups. 50% of the boys and 20% of the girls are in Group R. The rest of the students are in Group S.

1. What is the ratio of the number of students in Group S to Group R? Give your answer in the simplest form.
2. The number of girls in Group R is more than 30. What is the smallest possible total number of students taking part in the contest?

Boys		Girls
70 u		20 u
Group R	Group S	Group R	Group S
35 u	35 u	4 u	16 u

(a)
Boys : Girls
7 : 2
70 : 20

Number of boys in Group R
= 50% x 70 u
= ⁵⁰₁₀₀ x 70 u
= 35 u

Number of boys in Group S
= 70 u - 35 u
= 35 u

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

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

Group R : Group S
35 + 16 : 35 + 4 
51 : 39 _(÷3)
17 : 13

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

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

Number of sets of 4
= 30 ÷ 4
= 7 r 2

Since the number of girls in Group R is more than 30, the number of sets must be 1 more than 7.

1 u = 7 + 1 = 8

Smallest possible number of students
= 70 u + 20 u
= 90 u
= 90 x 8
= 720

Answer(s): (a) 17 : 13; (b) 720