PSLE
The number of girls and boys taking part in a quiz are in the ratio 1 : 8. These pupils are put into two teams. 10% of the girls and 30% of the boys are in Team P. The rest of the pupils are in Team Q.

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

Girls		Boys
10 u		80 u
Team P	Team Q	Team P	Team Q
1 u	9 u	24 u	56 u

(a)
Girls : Boys
1 : 8
10 : 80

Number of girls in Team P
= 10% x 10 u
= ¹⁰₁₀₀ x 10 u
= 1 u

Number of girls in Team Q
= 10 u - 1 u
= 9 u

Number of boys in Team P
= 30% x 80 u
= ³⁰₁₀₀ x 80 u
= 24 u

Number of boys in Team Q
= 80 u - 24 u
= 56 u

Team P : Team Q
9 + 56 : 1 + 24 
65 : 25 _(÷5)
13 : 5

(b)
Number of boys in Team P = 24 u

Since the number of boys in Team P is 24 u, it must be multiple of 24.

Number of sets of 24
= 90 ÷ 24
= 3 r 18

Since the number of boys in Team P is more than 90, the number of sets must be 1 more than 3.

1 u = 3 + 1 = 4

Smallest possible number of pupils
= 10 u + 80 u
= 90 u
= 90 x 4
= 360

Answer(s): (a) 13 : 5; (b) 360