PSLE
The number of boys and girls taking part in a test are in the ratio 5 : 4. These pupils are put into two groups. 60% of the boys and 30% of the girls are in Group F. The rest of the pupils are in Group G.

1. What is the ratio of the number of pupils in Group G to Group F? Give your answer in the simplest form.
2. The number of boys in Group G is fewer than 70. What is the largest possible total number of pupils taking part in the test?

Boys		Girls
50 u		40 u
Group F	Group G	Group F	Group G
30 u	20 u	12 u	28 u

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

Number of boys in Group F
= 60% x 50 u
= ⁶⁰₁₀₀ x 50 u
= 30 u

Number of boys in Group G
= 50 u - 30 u
= 20 u

Number of girls in Group F
= 30% x 40 u
= ³⁰₁₀₀ x 40 u
= 12 u

Number of girls in Group G
= 40 u - 12 u
= 28 u

Group G : Group F
20 + 28 : 30 + 12
48 : 42 _(÷6)
8 : 7

(b)
Number of boys in Group G = 20 u

Since the number of boys in Group G is 20 u, it must be multiple of 20.

Number of sets of 20
= 70 ÷ 20
= 3 r 10

Since the number of boys in Group G is less than 70, the number of sets must be 3.

1 u = 3

Largest possible number of pupils
= 50 u + 40 u
= 90 u
= 90 x 3
= 270

Answer(s): (a) 8 : 7; (b) 270