PSLE
The number of boys and girls taking part in a contest are in the ratio 6 : 7. These students are put into two groups. 20% of the boys and 40% of the girls are in Group F. The rest of the students are in Group G.

1. What is the ratio of the number of students in Group G to Group F? Give your answer in the simplest form.
2. The number of girls in Group F is more than 60. What is the smallest possible total number of students taking part in the contest?

Boys		Girls
60 u		70 u
Group F	Group G	Group F	Group G
12 u	48 u	28 u	42 u

(a)
Boys : Girls
6 : 7
60 : 70

Number of boys in Group F
= 20% x 60 u
= ²⁰₁₀₀ x 60 u
= 12 u

Number of boys in Group G
= 60 u - 12 u
= 48 u

Number of girls in Group F
= 40% x 70 u
= ⁴⁰₁₀₀ x 70 u
= 28 u

Number of girls in Group G
= 70 u - 28 u
= 42 u

Group F : Group G
48 + 42 : 12 + 28 
90 : 40 _(÷10)
9 : 4

(b)
Number of girls in Group F = 28 u

Since the number of girls in Group F is 28 u, it must be multiple of 28.

Number of sets of 28
= 60 ÷ 28
= 2 r 4

Since the number of girls in Group F is more than 60, the number of sets must be 1 more than 2.

1 u = 2 + 1 = 3

Smallest possible number of students
= 60 u + 70 u
= 130 u
= 130 x 3
= 390

Answer(s): (a) 9 : 4; (b) 390