PSLE
The number of girls and boys taking part in a contest are in the ratio 1 : 7. These students are put into two groups. 20% of the girls and 40% of the boys are in Group L. The rest of the students are in Group M.

1. What is the ratio of the number of students in Group M to Group L? Give your answer in the simplest form.
2. The number of girls in Group M is fewer than 90. What is the largest possible total number of students taking part in the contest?

Girls		Boys
10 u		70 u
Group L	Group M	Group L	Group M
2 u	8 u	28 u	42 u

(a)
Girls : Boys
1 : 7
10 : 70

Number of girls in Group L
= 20% x 10 u
= ²⁰₁₀₀ x 10 u
= 2 u

Number of girls in Group M
= 10 u - 2 u
= 8 u

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

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

Group M : Group L
8 + 42 : 2 + 28
50 : 30 _(÷10)
5 : 3

(b)
Number of girls in Group M = 8 u

Since the number of girls in Group M is 8 u, it must be multiple of 8.

Number of sets of 8
= 90 ÷ 8
= 11 r 2

Since the number of girls in Group M is less than 90, the number of sets must be 11.

1 u = 11

Largest possible number of students
= 10 u + 70 u
= 80 u
= 80 x 11
= 880

Answer(s): (a) 5 : 3; (b) 880