PSLE
The number of boys and girls taking part in a quiz are in the ratio 7 : 5. These students are put into two teams. 50% of the boys and 40% of the girls are in Team T. The rest of the students are in Team U.

1. What is the ratio of the number of students in Team U to Team T? Give your answer in the simplest form.
2. The number of boys in Team U is fewer than 90. What is the largest possible total number of students taking part in the quiz?

Boys		Girls
70 u		50 u
Team T	Team U	Team T	Team U
35 u	35 u	20 u	30 u

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

Number of boys in Team T
= 50% x 70 u
= ⁵⁰₁₀₀ x 70 u
= 35 u

Number of boys in Team U
= 70 u - 35 u
= 35 u

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

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

Team U : Team T
35 + 30 : 35 + 20
65 : 55 _(÷5)
13 : 11

(b)
Number of boys in Team U = 35 u

Since the number of boys in Team U is 35 u, it must be multiple of 35.

Number of sets of 35
= 90 ÷ 35
= 2 r 20

Since the number of boys in Team U is less than 90, the number of sets must be 2.

1 u = 2

Largest possible number of students
= 70 u + 50 u
= 120 u
= 120 x 2
= 240

Answer(s): (a) 13 : 11; (b) 240