PSLE
The number of boys and girls taking part in a test are in the ratio 2 : 7. These pupils are put into two teams. 20% of the boys and 50% 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 boys in Team R is fewer than 70. What is the largest possible total number of pupils taking part in the test?

Boys		Girls
20 u		70 u
Team Q	Team R	Team Q	Team R
4 u	16 u	35 u	35 u

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

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

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

Number of girls in Team Q
= 50% x 70 u
= ⁵⁰₁₀₀ x 70 u
= 35 u

Number of girls in Team R
= 70 u - 35 u
= 35 u

Team R : Team Q
16 + 35 : 4 + 35
51 : 39 _(÷3)
17 : 13

(b)
Number of boys in Team R = 16 u

Since the number of boys in Team R is 16 u, it must be multiple of 16.

Number of sets of 16
= 70 ÷ 16
= 4 r 6

Since the number of boys in Team R is less than 70, the number of sets must be 4.

1 u = 4

Largest possible number of pupils
= 20 u + 70 u
= 90 u
= 90 x 4
= 360

Answer(s): (a) 17 : 13; (b) 360