PSLE
The number of girls and boys taking part in a quiz are in the ratio 5 : 3. These students are put into two groups. 20% of the girls and 40% of the boys are in Group V. The rest of the students are in Group W.

1. What is the ratio of the number of students in Group W to Group V? Give your answer in the simplest form.
2. The number of boys in Group V is more than 50. What is the smallest possible total number of students taking part in the quiz?

Girls		Boys
50 u		30 u
Group V	Group W	Group V	Group W
10 u	40 u	12 u	18 u

(a)
Girls : Boys
5 : 3
50 : 30

Number of girls in Group V
= 20% x 50 u
= ²⁰₁₀₀ x 50 u
= 10 u

Number of girls in Group W
= 50 u - 10 u
= 40 u

Number of boys in Group V
= 40% x 30 u
= ⁴⁰₁₀₀ x 30 u
= 12 u

Number of boys in Group W
= 30 u - 12 u
= 18 u

Group V : Group W
40 + 18 : 10 + 12 
58 : 22 _(÷2)
29 : 11

(b)
Number of boys in Group V = 12 u

Since the number of boys in Group V is 12 u, it must be multiple of 12.

Number of sets of 12
= 50 ÷ 12
= 4 r 2

Since the number of boys in Group V is more than 50, the number of sets must be 1 more than 4.

1 u = 4 + 1 = 5

Smallest possible number of students
= 50 u + 30 u
= 80 u
= 80 x 5
= 400

Answer(s): (a) 29 : 11; (b) 400