PSLE
The number of boys and girls taking part in a quiz are in the ratio 1 : 3. These students are put into two groups. 60% of the boys and 30% of the girls are in Group T. The rest of the students are in Group U.

1. What is the ratio of the number of students in Group U to Group T? Give your answer in the simplest form.
2. The number of boys in Group U is fewer than 50. What is the largest possible total number of students taking part in the quiz?

Boys		Girls
10 u		30 u
Group T	Group U	Group T	Group U
6 u	4 u	9 u	21 u

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

Number of boys in Group T
= 60% x 10 u
= ⁶⁰₁₀₀ x 10 u
= 6 u

Number of boys in Group U
= 10 u - 6 u
= 4 u

Number of girls in Group T
= 30% x 30 u
= ³⁰₁₀₀ x 30 u
= 9 u

Number of girls in Group U
= 30 u - 9 u
= 21 u

Group U : Group T
4 + 21 : 6 + 9
25 : 15 _(÷5)
5 : 3

(b)
Number of boys in Group U = 4 u

Since the number of boys in Group U is 4 u, it must be multiple of 4.

Number of sets of 4
= 50 ÷ 4
= 12 r 2

Since the number of boys in Group U is less than 50, the number of sets must be 12.

1 u = 12

Largest possible number of students
= 10 u + 30 u
= 40 u
= 40 x 12
= 480

Answer(s): (a) 5 : 3; (b) 480