PSLE
The number of girls and boys taking part in a contest are in the ratio 4 : 3. These students are put into two groups. 40% of the girls and 30% of the boys 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 boys in Group X is more than 30. What is the smallest possible total number of students taking part in the contest?

Girls		Boys
40 u		30 u
Group X	Group Y	Group X	Group Y
16 u	24 u	9 u	21 u

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

Number of girls in Group X
= 40% x 40 u
= ⁴⁰₁₀₀ x 40 u
= 16 u

Number of girls in Group Y
= 40 u - 16 u
= 24 u

Number of boys in Group X
= 30% x 30 u
= ³⁰₁₀₀ x 30 u
= 9 u

Number of boys in Group Y
= 30 u - 9 u
= 21 u

Group X : Group Y
24 + 21 : 16 + 9 
45 : 25 _(÷5)
9 : 5

(b)
Number of boys in Group X = 9 u

Since the number of boys in Group X is 9 u, it must be multiple of 9.

Number of sets of 9
= 30 ÷ 9
= 3 r 3

Since the number of boys in Group X is more than 30, the number of sets must be 1 more than 3.

1 u = 3 + 1 = 4

Smallest possible number of students
= 40 u + 30 u
= 70 u
= 70 x 4
= 280

Answer(s): (a) 9 : 5; (b) 280