PSLE
The number of girls and boys taking part in a quiz are in the ratio 7 : 5. These pupils are put into two teams. 60% 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 80. What is the smallest possible total number of pupils taking part in the quiz?

Girls		Boys
70 u		50 u
Team P	Team Q	Team P	Team Q
42 u	28 u	15 u	35 u

(a)
Girls : Boys
7 : 5
70 : 50

Number of girls in Team P
= 60% x 70 u
= ⁶⁰₁₀₀ x 70 u
= 42 u

Number of girls in Team Q
= 70 u - 42 u
= 28 u

Number of boys in Team P
= 30% x 50 u
= ³⁰₁₀₀ x 50 u
= 15 u

Number of boys in Team Q
= 50 u - 15 u
= 35 u

Team P : Team Q
28 + 35 : 42 + 15 
63 : 57 _(÷3)
21 : 19

(b)
Number of boys in Team P = 15 u

Since the number of boys in Team P is 15 u, it must be multiple of 15.

Number of sets of 15
= 80 ÷ 15
= 5 r 5

Since the number of boys in Team P is more than 80, the number of sets must be 1 more than 5.

1 u = 5 + 1 = 6

Smallest possible number of pupils
= 70 u + 50 u
= 120 u
= 120 x 6
= 720

Answer(s): (a) 21 : 19; (b) 720