PSLE
The number of girls and boys taking part in a quiz are in the ratio 1 : 2. These students are put into two groups. 40% of the girls and 20% of the boys are in Group W. The rest of the students are in Group X.

1. What is the ratio of the number of students in Group X to Group W? Give your answer in the simplest form.
2. The number of boys in Group W is more than 70. What is the smallest possible total number of students taking part in the quiz?

Girls		Boys
10 u		20 u
Group W	Group X	Group W	Group X
4 u	6 u	4 u	16 u

(a)
Girls : Boys
1 : 2
10 : 20

Number of girls in Group W
= 40% x 10 u
= ⁴⁰₁₀₀ x 10 u
= 4 u

Number of girls in Group X
= 10 u - 4 u
= 6 u

Number of boys in Group W
= 20% x 20 u
= ²⁰₁₀₀ x 20 u
= 4 u

Number of boys in Group X
= 20 u - 4 u
= 16 u

Group W : Group X
6 + 16 : 4 + 4 
22 : 8 _(÷2)
11 : 4

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

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

Number of sets of 4
= 70 ÷ 4
= 17 r 2

Since the number of boys in Group W is more than 70, the number of sets must be 1 more than 17.

1 u = 17 + 1 = 18

Smallest possible number of students
= 10 u + 20 u
= 30 u
= 30 x 18
= 540

Answer(s): (a) 11 : 4; (b) 540