PSLE
The number of boys and girls taking part in a contest are in the ratio 1 : 6. These students are put into two groups. 20% 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 girls in Group C is more than 80. What is the smallest possible total number of students taking part in the contest?

Boys		Girls
10 u		60 u
Group C	Group D	Group C	Group D
2 u	8 u	18 u	42 u

(a)
Boys : Girls
1 : 6
10 : 60

Number of boys in Group C
= 20% x 10 u
= ²⁰₁₀₀ x 10 u
= 2 u

Number of boys in Group D
= 10 u - 2 u
= 8 u

Number of girls in Group C
= 30% x 60 u
= ³⁰₁₀₀ x 60 u
= 18 u

Number of girls in Group D
= 60 u - 18 u
= 42 u

Group C : Group D
8 + 42 : 2 + 18 
50 : 20 _(÷10)
5 : 2

(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
= 80 ÷ 18
= 4 r 8

Since the number of girls in Group C is more than 80, the number of sets must be 1 more than 4.

1 u = 4 + 1 = 5

Smallest possible number of students
= 10 u + 60 u
= 70 u
= 70 x 5
= 350

Answer(s): (a) 5 : 2; (b) 350