PSLE
The number of boys and girls taking part in a contest are in the ratio 3 : 8. These students are put into two groups. 20% of the boys and 40% of the girls are in Group G. The rest of the students are in Group H.

1. What is the ratio of the number of students in Group H to Group G? Give your answer in the simplest form.
2. The number of boys in Group H is fewer than 50. What is the largest possible total number of students taking part in the contest?

Boys		Girls
30 u		80 u
Group G	Group H	Group G	Group H
6 u	24 u	32 u	48 u

(a)
Boys : Girls
3 : 8
30 : 80

Number of boys in Group G
= 20% x 30 u
= ²⁰₁₀₀ x 30 u
= 6 u

Number of boys in Group H
= 30 u - 6 u
= 24 u

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

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

Group H : Group G
24 + 48 : 6 + 32
72 : 38 _(÷2)
36 : 19

(b)
Number of boys in Group H = 24 u

Since the number of boys in Group H is 24 u, it must be multiple of 24.

Number of sets of 24
= 50 ÷ 24
= 2 r 2

Since the number of boys in Group H is less than 50, the number of sets must be 2.

1 u = 2

Largest possible number of students
= 30 u + 80 u
= 110 u
= 110 x 2
= 220

Answer(s): (a) 36 : 19; (b) 220