PSLE
The number of boys and girls taking part in a test are in the ratio 7 : 2. These pupils are put into two teams. 30% of the boys and 20% of the girls are in Team Q. The rest of the pupils are in Team R.

1. What is the ratio of the number of pupils in Team R to Team Q? Give your answer in the simplest form.
2. The number of girls in Team Q is more than 90. What is the smallest possible total number of pupils taking part in the test?

Boys		Girls
70 u		20 u
Team Q	Team R	Team Q	Team R
21 u	49 u	4 u	16 u

(a)
Boys : Girls
7 : 2
70 : 20

Number of boys in Team Q
= 30% x 70 u
= ³⁰₁₀₀ x 70 u
= 21 u

Number of boys in Team R
= 70 u - 21 u
= 49 u

Number of girls in Team Q
= 20% x 20 u
= ²⁰₁₀₀ x 20 u
= 4 u

Number of girls in Team R
= 20 u - 4 u
= 16 u

Team Q : Team R
49 + 16 : 21 + 4 
65 : 25 _(÷5)
13 : 5

(b)
Number of girls in Team Q = 4 u

Since the number of girls in Team Q is 4 u, it must be multiple of 4.

Number of sets of 4
= 90 ÷ 4
= 22 r 2

Since the number of girls in Team Q is more than 90, the number of sets must be 1 more than 22.

1 u = 22 + 1 = 23

Smallest possible number of pupils
= 70 u + 20 u
= 90 u
= 90 x 23
= 2070

Answer(s): (a) 13 : 5; (b) 2070