PSLE
The number of boys and girls taking part in a quiz are in the ratio 1 : 8. These students are put into two groups. 60% 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 boys in Group G is fewer than 90. What is the largest possible total number of students taking part in the quiz?

Boys		Girls
10 u		80 u
Group F	Group G	Group F	Group G
6 u	4 u	32 u	48 u

(a)
Boys : Girls
1 : 8
10 : 80

Number of boys in Group F
= 60% x 10 u
= ⁶⁰₁₀₀ x 10 u
= 6 u

Number of boys in Group G
= 10 u - 6 u
= 4 u

Number of girls in Group F
= 40% x 80 u
= ⁴⁰₁₀₀ x 80 u
= 32 u

Number of girls in Group G
= 80 u - 32 u
= 48 u

Group G : Group F
4 + 48 : 6 + 32
52 : 38 _(÷2)
26 : 19

(b)
Number of boys in Group G = 4 u

Since the number of boys in Group G is 4 u, it must be multiple of 4.

Number of sets of 4
= 90 ÷ 4
= 22 r 2

Since the number of boys in Group G is less than 90, the number of sets must be 22.

1 u = 22

Largest possible number of students
= 10 u + 80 u
= 90 u
= 90 x 22
= 1980

Answer(s): (a) 26 : 19; (b) 1980