PSLE
The number of girls and boys taking part in a contest are in the ratio 1 : 3. These pupils are put into two teams. 10% of the girls and 50% of the boys are in Team X. The rest of the pupils are in Team Y.

1. What is the ratio of the number of pupils in Team Y to Team X? Give your answer in the simplest form.
2. The number of boys in Team X is more than 80. What is the smallest possible total number of pupils taking part in the contest?

Girls		Boys
10 u		30 u
Team X	Team Y	Team X	Team Y
1 u	9 u	15 u	15 u

(a)
Girls : Boys
1 : 3
10 : 30

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

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

Number of boys in Team X
= 50% x 30 u
= ⁵⁰₁₀₀ x 30 u
= 15 u

Number of boys in Team Y
= 30 u - 15 u
= 15 u

Team X : Team Y
9 + 15 : 1 + 15 
24 : 16 _(÷8)
3 : 2

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

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

1 u = 5 + 1 = 6

Smallest possible number of pupils
= 10 u + 30 u
= 40 u
= 40 x 6
= 240

Answer(s): (a) 3 : 2; (b) 240