PSLE
The number of girls and boys taking part in a quiz are in the ratio 2 : 3. These pupils are put into two groups. 30% of the girls and 60% of the boys are in Group H. The rest of the pupils are in Group J.

1. What is the ratio of the number of pupils in Group J to Group H? Give your answer in the simplest form.
2. The number of girls in Group J is fewer than 40. What is the largest possible total number of pupils taking part in the quiz?

Girls		Boys
20 u		30 u
Group H	Group J	Group H	Group J
6 u	14 u	18 u	12 u

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

Number of girls in Group H
= 30% x 20 u
= ³⁰₁₀₀ x 20 u
= 6 u

Number of girls in Group J
= 20 u - 6 u
= 14 u

Number of boys in Group H
= 60% x 30 u
= ⁶⁰₁₀₀ x 30 u
= 18 u

Number of boys in Group J
= 30 u - 18 u
= 12 u

Group J : Group H
14 + 12 : 6 + 18
26 : 24 _(÷2)
13 : 12

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

Since the number of girls in Group J 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 J is less than 40, the number of sets must be 2.

1 u = 2

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

Answer(s): (a) 13 : 12; (b) 100