PSLE
The number of girls and boys taking part in a contest are in the ratio 1 : 8. These students are put into two groups. 70% of the girls and 40% 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 girls in Group X is fewer than 40. What is the largest possible total number of students taking part in the contest?

Girls		Boys
10 u		80 u
Group W	Group X	Group W	Group X
7 u	3 u	32 u	48 u

(a)
Girls : Boys
1 : 8
10 : 80

Number of girls in Group W
= 70% x 10 u
= ⁷⁰₁₀₀ x 10 u
= 7 u

Number of girls in Group X
= 10 u - 7 u
= 3 u

Number of boys in Group W
= 40% x 80 u
= ⁴⁰₁₀₀ x 80 u
= 32 u

Number of boys in Group X
= 80 u - 32 u
= 48 u

Group X : Group W
3 + 48 : 7 + 32
51 : 39 _(÷3)
17 : 13

(b)
Number of girls in Group X = 3 u

Since the number of girls in Group X is 3 u, it must be multiple of 3.

Number of sets of 3
= 40 ÷ 3
= 13 r 1

Since the number of girls in Group X is less than 40, the number of sets must be 13.

1 u = 13

Largest possible number of students
= 10 u + 80 u
= 90 u
= 90 x 13
= 1170

Answer(s): (a) 17 : 13; (b) 1170