PSLE
The number of boys and girls taking part in a quiz are in the ratio 2 : 7. These pupils are put into two groups. 60% of the boys and 20% of the girls 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 girls in Group G is more than 40. What is the smallest possible total number of pupils taking part in the quiz?

Boys		Girls
20 u		70 u
Group G	Group H	Group G	Group H
12 u	8 u	14 u	56 u

(a)
Boys : Girls
2 : 7
20 : 70

Number of boys in Group G
= 60% x 20 u
= ⁶⁰₁₀₀ x 20 u
= 12 u

Number of boys in Group H
= 20 u - 12 u
= 8 u

Number of girls in Group G
= 20% x 70 u
= ²⁰₁₀₀ x 70 u
= 14 u

Number of girls in Group H
= 70 u - 14 u
= 56 u

Group G : Group H
8 + 56 : 12 + 14 
64 : 26 _(÷2)
32 : 13

(b)
Number of girls in Group G = 14 u

Since the number of girls in Group G is 14 u, it must be multiple of 14.

Number of sets of 14
= 40 ÷ 14
= 2 r 12

Since the number of girls in Group G is more than 40, the number of sets must be 1 more than 2.

1 u = 2 + 1 = 3

Smallest possible number of pupils
= 20 u + 70 u
= 90 u
= 90 x 3
= 270

Answer(s): (a) 32 : 13; (b) 270