PSLE
The number of girls and boys taking part in a quiz are in the ratio 3 : 8. These students are put into two groups. 40% of the girls and 30% of the boys are in Group P. The rest of the students are in Group Q.

1. What is the ratio of the number of students in Group Q to Group P? Give your answer in the simplest form.
2. The number of girls in Group Q is fewer than 70. What is the largest possible total number of students taking part in the quiz?

Girls		Boys
30 u		80 u
Group P	Group Q	Group P	Group Q
12 u	18 u	24 u	56 u

(a)
Girls : Boys
3 : 8
30 : 80

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

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

Number of boys in Group P
= 30% x 80 u
= ³⁰₁₀₀ x 80 u
= 24 u

Number of boys in Group Q
= 80 u - 24 u
= 56 u

Group Q : Group P
18 + 56 : 12 + 24
74 : 36 _(÷2)
37 : 18

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

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

Number of sets of 18
= 70 ÷ 18
= 3 r 16

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

1 u = 3

Largest possible number of students
= 30 u + 80 u
= 110 u
= 110 x 3
= 330

Answer(s): (a) 37 : 18; (b) 330