PSLE
The number of boys and girls taking part in a contest are in the ratio 7 : 3. These students are put into two groups. 60% of the boys and 10% of the girls are in Group Y. The rest of the students are in Group Z.

1. What is the ratio of the number of students in Group Z to Group Y? Give your answer in the simplest form.
2. The number of girls in Group Y is more than 80. What is the smallest possible total number of students taking part in the contest?

Boys		Girls
70 u		30 u
Group Y	Group Z	Group Y	Group Z
42 u	28 u	3 u	27 u

(a)
Boys : Girls
7 : 3
70 : 30

Number of boys in Group Y
= 60% x 70 u
= ⁶⁰₁₀₀ x 70 u
= 42 u

Number of boys in Group Z
= 70 u - 42 u
= 28 u

Number of girls in Group Y
= 10% x 30 u
= ¹⁰₁₀₀ x 30 u
= 3 u

Number of girls in Group Z
= 30 u - 3 u
= 27 u

Group Y : Group Z
28 + 27 : 42 + 3 
55 : 45 _(÷5)
11 : 9

(b)
Number of girls in Group Y = 3 u

Since the number of girls in Group Y is 3 u, it must be multiple of 3.

Number of sets of 3
= 80 ÷ 3
= 26 r 2

Since the number of girls in Group Y is more than 80, the number of sets must be 1 more than 26.

1 u = 26 + 1 = 27

Smallest possible number of students
= 70 u + 30 u
= 100 u
= 100 x 27
= 2700

Answer(s): (a) 11 : 9; (b) 2700