PSLE
The number of girls and boys taking part in a test are in the ratio 1 : 3. These students are put into two groups. 30% of the girls and 50% of the boys are in Group K. The rest of the students are in Group L.

1. What is the ratio of the number of students in Group L to Group K? Give your answer in the simplest form.
2. The number of boys in Group K is more than 40. What is the smallest possible total number of students taking part in the test?

Girls		Boys
10 u		30 u
Group K	Group L	Group K	Group L
3 u	7 u	15 u	15 u

(a)
Girls : Boys
1 : 3
10 : 30

Number of girls in Group K
= 30% x 10 u
= ³⁰₁₀₀ x 10 u
= 3 u

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

Number of boys in Group K
= 50% x 30 u
= ⁵⁰₁₀₀ x 30 u
= 15 u

Number of boys in Group L
= 30 u - 15 u
= 15 u

Group K : Group L
7 + 15 : 3 + 15 
22 : 18 _(÷2)
11 : 9

(b)
Number of boys in Group K = 15 u

Since the number of boys in Group K is 15 u, it must be multiple of 15.

Number of sets of 15
= 40 ÷ 15
= 2 r 10

Since the number of boys in Group K is more than 40, the number of sets must be 1 more than 2.

1 u = 2 + 1 = 3

Smallest possible number of students
= 10 u + 30 u
= 40 u
= 40 x 3
= 120

Answer(s): (a) 11 : 9; (b) 120