PSLE
The number of boys and girls taking part in a contest are in the ratio 3 : 7. These pupils are put into two teams. 60% of the boys and 20% of the girls are in Team D. The rest of the pupils are in Team E.

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

Boys		Girls
30 u		70 u
Team D	Team E	Team D	Team E
18 u	12 u	14 u	56 u

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

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

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

Number of girls in Team D
= 20% x 70 u
= ²⁰₁₀₀ x 70 u
= 14 u

Number of girls in Team E
= 70 u - 14 u
= 56 u

Team E : Team D
12 + 56 : 18 + 14
68 : 32 _(÷4)
17 : 8

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

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

1 u = 4

Largest possible number of pupils
= 30 u + 70 u
= 100 u
= 100 x 4
= 400

Answer(s): (a) 17 : 8; (b) 400