PSLE
The number of girls and boys taking part in a quiz are in the ratio 3 : 4. These students are put into two teams. 80% of the girls and 10% of the boys are in Team P. The rest of the students are in Team Q.

1. What is the ratio of the number of students in Team Q to Team P? Give your answer in the simplest form.
2. The number of boys in Team P is more than 70. What is the smallest possible total number of students taking part in the quiz?

Girls		Boys
30 u		40 u
Team P	Team Q	Team P	Team Q
24 u	6 u	4 u	36 u

(a)
Girls : Boys
3 : 4
30 : 40

Number of girls in Team P
= 80% x 30 u
= ⁸⁰₁₀₀ x 30 u
= 24 u

Number of girls in Team Q
= 30 u - 24 u
= 6 u

Number of boys in Team P
= 10% x 40 u
= ¹⁰₁₀₀ x 40 u
= 4 u

Number of boys in Team Q
= 40 u - 4 u
= 36 u

Team P : Team Q
6 + 36 : 24 + 4 
42 : 28 _(÷14)
3 : 2

(b)
Number of boys in Team P = 4 u

Since the number of boys in Team P is 4 u, it must be multiple of 4.

Number of sets of 4
= 70 ÷ 4
= 17 r 2

Since the number of boys in Team P is more than 70, the number of sets must be 1 more than 17.

1 u = 17 + 1 = 18

Smallest possible number of students
= 30 u + 40 u
= 70 u
= 70 x 18
= 1260

Answer(s): (a) 3 : 2; (b) 1260