PSLE
The number of boys and girls taking part in a test are in the ratio 7 : 3. These students are put into two groups. 40% of the boys and 20% of the girls are in Group A. The rest of the students are in Group B.

1. What is the ratio of the number of students in Group B to Group A? Give your answer in the simplest form.
2. The number of girls in Group A is more than 80. What is the smallest possible total number of students taking part in the test?

Boys		Girls
70 u		30 u
Group A	Group B	Group A	Group B
28 u	42 u	6 u	24 u

(a)
Boys : Girls
7 : 3
70 : 30

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

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

Number of girls in Group A
= 20% x 30 u
= ²⁰₁₀₀ x 30 u
= 6 u

Number of girls in Group B
= 30 u - 6 u
= 24 u

Group A : Group B
42 + 24 : 28 + 6 
66 : 34 _(÷2)
33 : 17

(b)
Number of girls in Group A = 6 u

Since the number of girls in Group A is 6 u, it must be multiple of 6.

Number of sets of 6
= 80 ÷ 6
= 13 r 2

Since the number of girls in Group A is more than 80, the number of sets must be 1 more than 13.

1 u = 13 + 1 = 14

Smallest possible number of students
= 70 u + 30 u
= 100 u
= 100 x 14
= 1400

Answer(s): (a) 33 : 17; (b) 1400