PSLE
The number of boys and girls taking part in a quiz are in the ratio 1 : 8. These students are put into two groups. 70% of the boys and 40% of the girls are in Group X. The rest of the students are in Group Y.

1. What is the ratio of the number of students in Group Y to Group X? Give your answer in the simplest form.
2. The number of girls in Group X is more than 70. What is the smallest possible total number of students taking part in the quiz?

Boys		Girls
10 u		80 u
Group X	Group Y	Group X	Group Y
7 u	3 u	32 u	48 u

(a)
Boys : Girls
1 : 8
10 : 80

Number of boys in Group X
= 70% x 10 u
= ⁷⁰₁₀₀ x 10 u
= 7 u

Number of boys in Group Y
= 10 u - 7 u
= 3 u

Number of girls in Group X
= 40% x 80 u
= ⁴⁰₁₀₀ x 80 u
= 32 u

Number of girls in Group Y
= 80 u - 32 u
= 48 u

Group X : Group Y
3 + 48 : 7 + 32 
51 : 39 _(÷3)
17 : 13

(b)
Number of girls in Group X = 32 u

Since the number of girls in Group X is 32 u, it must be multiple of 32.

Number of sets of 32
= 70 ÷ 32
= 2 r 6

Since the number of girls in Group X is more than 70, the number of sets must be 1 more than 2.

1 u = 2 + 1 = 3

Smallest possible number of students
= 10 u + 80 u
= 90 u
= 90 x 3
= 270

Answer(s): (a) 17 : 13; (b) 270