PSLE
The number of boys and girls taking part in a test are in the ratio 6 : 7. These pupils are put into two teams. 70% of the boys and 20% of the girls are in Team Y. The rest of the pupils are in Team Z.

1. What is the ratio of the number of pupils in Team Z to Team Y? Give your answer in the simplest form.
2. The number of girls in Team Y is more than 40. What is the smallest possible total number of pupils taking part in the test?

Boys		Girls
60 u		70 u
Team Y	Team Z	Team Y	Team Z
42 u	18 u	14 u	56 u

(a)
Boys : Girls
6 : 7
60 : 70

Number of boys in Team Y
= 70% x 60 u
= ⁷⁰₁₀₀ x 60 u
= 42 u

Number of boys in Team Z
= 60 u - 42 u
= 18 u

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

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

Team Y : Team Z
18 + 56 : 42 + 14 
74 : 56 _(÷2)
37 : 28

(b)
Number of girls in Team Y = 14 u

Since the number of girls in Team Y is 14 u, it must be multiple of 14.

Number of sets of 14
= 40 ÷ 14
= 2 r 12

Since the number of girls in Team Y is more than 40, the number of sets must be 1 more than 2.

1 u = 2 + 1 = 3

Smallest possible number of pupils
= 60 u + 70 u
= 130 u
= 130 x 3
= 390

Answer(s): (a) 37 : 28; (b) 390