PSLE
The number of boys and girls taking part in a contest are in the ratio 4 : 5. These students are put into two teams. 80% of the boys and 20% of the girls are in Team Y. The rest of the students are in Team Z.

1. What is the ratio of the number of students in Team Z to Team Y? Give your answer in the simplest form.
2. The number of boys in Team Z is fewer than 30. What is the largest possible total number of students taking part in the contest?

Boys		Girls
40 u		50 u
Team Y	Team Z	Team Y	Team Z
32 u	8 u	10 u	40 u

(a)
Boys : Girls
4 : 5
40 : 50

Number of boys in Team Y
= 80% x 40 u
= ⁸⁰₁₀₀ x 40 u
= 32 u

Number of boys in Team Z
= 40 u - 32 u
= 8 u

Number of girls in Team Y
= 20% x 50 u
= ²⁰₁₀₀ x 50 u
= 10 u

Number of girls in Team Z
= 50 u - 10 u
= 40 u

Team Z : Team Y
8 + 40 : 32 + 10
48 : 42 _(÷6)
8 : 7

(b)
Number of boys in Team Z = 8 u

Since the number of boys in Team Z is 8 u, it must be multiple of 8.

Number of sets of 8
= 30 ÷ 8
= 3 r 6

Since the number of boys in Team Z is less than 30, the number of sets must be 3.

1 u = 3

Largest possible number of students
= 40 u + 50 u
= 90 u
= 90 x 3
= 270

Answer(s): (a) 8 : 7; (b) 270