PSLE
The number of boys and girls taking part in a contest are in the ratio 3 : 8. These pupils are put into two teams. 60% of the boys and 30% of the girls are in Team J. The rest of the pupils are in Team K.

1. What is the ratio of the number of pupils in Team K to Team J? Give your answer in the simplest form.
2. The number of boys in Team K is fewer than 50. What is the largest possible total number of pupils taking part in the contest?

Boys		Girls
30 u		80 u
Team J	Team K	Team J	Team K
18 u	12 u	24 u	56 u

(a)
Boys : Girls
3 : 8
30 : 80

Number of boys in Team J
= 60% x 30 u
= ⁶⁰₁₀₀ x 30 u
= 18 u

Number of boys in Team K
= 30 u - 18 u
= 12 u

Number of girls in Team J
= 30% x 80 u
= ³⁰₁₀₀ x 80 u
= 24 u

Number of girls in Team K
= 80 u - 24 u
= 56 u

Team K : Team J
12 + 56 : 18 + 24
68 : 42 _(÷2)
34 : 21

(b)
Number of boys in Team K = 12 u

Since the number of boys in Team K is 12 u, it must be multiple of 12.

Number of sets of 12
= 50 ÷ 12
= 4 r 2

Since the number of boys in Team K is less than 50, the number of sets must be 4.

1 u = 4

Largest possible number of pupils
= 30 u + 80 u
= 110 u
= 110 x 4
= 440

Answer(s): (a) 34 : 21; (b) 440