PSLE
The number of boys and girls taking part in a contest are in the ratio 7 : 4. These students are put into two teams. 40% of the boys and 50% of the girls are in Team A. The rest of the students are in Team B.

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

Boys		Girls
70 u		40 u
Team A	Team B	Team A	Team B
28 u	42 u	20 u	20 u

(a)
Boys : Girls
7 : 4
70 : 40

Number of boys in Team A
= 40% x 70 u
= ⁴⁰₁₀₀ x 70 u
= 28 u

Number of boys in Team B
= 70 u - 28 u
= 42 u

Number of girls in Team A
= 50% x 40 u
= ⁵⁰₁₀₀ x 40 u
= 20 u

Number of girls in Team B
= 40 u - 20 u
= 20 u

Team A : Team B
42 + 20 : 28 + 20 
62 : 48 _(÷2)
31 : 24

(b)
Number of girls in Team A = 20 u

Since the number of girls in Team A is 20 u, it must be multiple of 20.

Number of sets of 20
= 90 ÷ 20
= 4 r 10

Since the number of girls in Team A is more than 90, the number of sets must be 1 more than 4.

1 u = 4 + 1 = 5

Smallest possible number of students
= 70 u + 40 u
= 110 u
= 110 x 5
= 550

Answer(s): (a) 31 : 24; (b) 550