PSLE
The number of girls and boys taking part in a contest are in the ratio 3 : 2. These pupils are put into two groups. 40% of the girls and 30% of the boys are in Group B. The rest of the pupils are in Group C.

1. What is the ratio of the number of pupils in Group C to Group B? Give your answer in the simplest form.
2. The number of girls in Group C is fewer than 50. What is the largest possible total number of pupils taking part in the contest?

Girls		Boys
30 u		20 u
Group B	Group C	Group B	Group C
12 u	18 u	6 u	14 u

(a)
Girls : Boys
3 : 2
30 : 20

Number of girls in Group B
= 40% x 30 u
= ⁴⁰₁₀₀ x 30 u
= 12 u

Number of girls in Group C
= 30 u - 12 u
= 18 u

Number of boys in Group B
= 30% x 20 u
= ³⁰₁₀₀ x 20 u
= 6 u

Number of boys in Group C
= 20 u - 6 u
= 14 u

Group C : Group B
18 + 14 : 12 + 6
32 : 18 _(÷2)
16 : 9

(b)
Number of girls in Group C = 18 u

Since the number of girls in Group C is 18 u, it must be multiple of 18.

Number of sets of 18
= 50 ÷ 18
= 2 r 14

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

1 u = 2

Largest possible number of pupils
= 30 u + 20 u
= 50 u
= 50 x 2
= 100

Answer(s): (a) 16 : 9; (b) 100