PSLE
The number of boys and girls taking part in a quiz are in the ratio 3 : 4. These students are put into two teams. 60% of the boys and 10% of the girls are in Team J. The rest of the students are in Team K.

1. What is the ratio of the number of students in Team K to Team J? Give your answer in the simplest form.
2. The number of girls in Team J is more than 90. What is the smallest possible total number of students taking part in the quiz?

Boys		Girls
30 u		40 u
Team J	Team K	Team J	Team K
18 u	12 u	4 u	36 u

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

Number of boys in Team J
= 60% x 30 u
= ⁶⁰₁₀₀ x 30 u
= 18 u

Number of boys in Team K
= 30 u - 18 u
= 12 u

Number of girls in Team J
= 10% x 40 u
= ¹⁰₁₀₀ x 40 u
= 4 u

Number of girls in Team K
= 40 u - 4 u
= 36 u

Team J : Team K
12 + 36 : 18 + 4 
48 : 22 _(÷2)
24 : 11

(b)
Number of girls in Team J = 4 u

Since the number of girls in Team J is 4 u, it must be multiple of 4.

Number of sets of 4
= 90 ÷ 4
= 22 r 2

Since the number of girls in Team J is more than 90, the number of sets must be 1 more than 22.

1 u = 22 + 1 = 23

Smallest possible number of students
= 30 u + 40 u
= 70 u
= 70 x 23
= 1610

Answer(s): (a) 24 : 11; (b) 1610