PSLE
The number of boys and girls taking part in a quiz are in the ratio 1 : 5. These students are put into two teams. 10% of the boys and 40% 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 boys in Team K is fewer than 70. What is the largest possible total number of students taking part in the quiz?

Boys		Girls
10 u		50 u
Team J	Team K	Team J	Team K
1 u	9 u	20 u	30 u

(a)
Boys : Girls
1 : 5
10 : 50

Number of boys in Team J
= 10% x 10 u
= ¹⁰₁₀₀ x 10 u
= 1 u

Number of boys in Team K
= 10 u - 1 u
= 9 u

Number of girls in Team J
= 40% x 50 u
= ⁴⁰₁₀₀ x 50 u
= 20 u

Number of girls in Team K
= 50 u - 20 u
= 30 u

Team K : Team J
9 + 30 : 1 + 20
39 : 21 _(÷3)
13 : 7

(b)
Number of boys in Team K = 9 u

Since the number of boys in Team K is 9 u, it must be multiple of 9.

Number of sets of 9
= 70 ÷ 9
= 7 r 7

Since the number of boys in Team K is less than 70, the number of sets must be 7.

1 u = 7

Largest possible number of students
= 10 u + 50 u
= 60 u
= 60 x 7
= 420

Answer(s): (a) 13 : 7; (b) 420