PSLE
The number of girls and boys taking part in a contest are in the ratio 7 : 4. These students are put into two groups. 40% of the girls and 60% of the boys 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 G is more than 70. What is the smallest possible total number of students taking part in the contest?

Girls		Boys
70 u		40 u
Group G	Group H	Group G	Group H
28 u	42 u	24 u	16 u

(a)
Girls : Boys
7 : 4
70 : 40

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

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

Number of boys in Group G
= 60% x 40 u
= ⁶⁰₁₀₀ x 40 u
= 24 u

Number of boys in Group H
= 40 u - 24 u
= 16 u

Group G : Group H
42 + 16 : 28 + 24 
58 : 52 _(÷2)
29 : 26

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

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

Number of sets of 24
= 70 ÷ 24
= 2 r 22

Since the number of boys in Group G is more than 70, the number of sets must be 1 more than 2.

1 u = 2 + 1 = 3

Smallest possible number of students
= 70 u + 40 u
= 110 u
= 110 x 3
= 330

Answer(s): (a) 29 : 26; (b) 330