PSLE
The number of girls and boys taking part in a test are in the ratio 3 : 8. These students are put into two groups. 40% of the girls and 30% of the boys are in Group N. The rest of the students are in Group P.

1. What is the ratio of the number of students in Group P to Group N? Give your answer in the simplest form.
2. The number of boys in Group N is more than 60. What is the smallest possible total number of students taking part in the test?

Girls		Boys
30 u		80 u
Group N	Group P	Group N	Group P
12 u	18 u	24 u	56 u

(a)
Girls : Boys
3 : 8
30 : 80

Number of girls in Group N
= 40% x 30 u
= ⁴⁰₁₀₀ x 30 u
= 12 u

Number of girls in Group P
= 30 u - 12 u
= 18 u

Number of boys in Group N
= 30% x 80 u
= ³⁰₁₀₀ x 80 u
= 24 u

Number of boys in Group P
= 80 u - 24 u
= 56 u

Group N : Group P
18 + 56 : 12 + 24 
74 : 36 _(÷2)
37 : 18

(b)
Number of boys in Group N = 24 u

Since the number of boys in Group N is 24 u, it must be multiple of 24.

Number of sets of 24
= 60 ÷ 24
= 2 r 12

Since the number of boys in Group N is more than 60, the number of sets must be 1 more than 2.

1 u = 2 + 1 = 3

Smallest possible number of students
= 30 u + 80 u
= 110 u
= 110 x 3
= 330

Answer(s): (a) 37 : 18; (b) 330