PSLE
The number of girls and boys taking part in a test are in the ratio 5 : 4. These pupils are put into two groups. 20% of the girls and 30% of the boys are in Group G. The rest of the pupils are in Group H.

1. What is the ratio of the number of pupils in Group H to Group G? Give your answer in the simplest form.
2. The number of boys in Group G is more than 50. What is the smallest possible total number of pupils taking part in the test?

Girls		Boys
50 u		40 u
Group G	Group H	Group G	Group H
10 u	40 u	12 u	28 u

(a)
Girls : Boys
5 : 4
50 : 40

Number of girls in Group G
= 20% x 50 u
= ²⁰₁₀₀ x 50 u
= 10 u

Number of girls in Group H
= 50 u - 10 u
= 40 u

Number of boys in Group G
= 30% x 40 u
= ³⁰₁₀₀ x 40 u
= 12 u

Number of boys in Group H
= 40 u - 12 u
= 28 u

Group G : Group H
40 + 28 : 10 + 12 
68 : 22 _(÷2)
34 : 11

(b)
Number of boys in Group G = 12 u

Since the number of boys in Group G is 12 u, it must be multiple of 12.

Number of sets of 12
= 50 ÷ 12
= 4 r 2

Since the number of boys in Group G is more than 50, the number of sets must be 1 more than 4.

1 u = 4 + 1 = 5

Smallest possible number of pupils
= 50 u + 40 u
= 90 u
= 90 x 5
= 450

Answer(s): (a) 34 : 11; (b) 450