PSLE
The number of boys and girls taking part in a quiz are in the ratio 3 : 4. These students are put into two groups. 60% of the boys and 30% of the girls are in Group C. The rest of the students are in Group D.

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

Boys		Girls
30 u		40 u
Group C	Group D	Group C	Group D
18 u	12 u	12 u	28 u

(a)
Boys : Girls
3 : 4
30 : 40

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

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

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

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

Group D : Group C
12 + 28 : 18 + 12
40 : 30 _(÷10)
4 : 3

(b)
Number of boys in Group D = 12 u

Since the number of boys in Group D is 12 u, it must be multiple of 12.

Number of sets of 12
= 70 ÷ 12
= 5 r 10

Since the number of boys in Group D is less than 70, the number of sets must be 5.

1 u = 5

Largest possible number of students
= 30 u + 40 u
= 70 u
= 70 x 5
= 350

Answer(s): (a) 4 : 3; (b) 350