PSLE
The number of girls and boys taking part in a quiz are in the ratio 1 : 4. These students are put into two groups. 80% of the girls and 10% 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 90. What is the smallest possible total number of students taking part in the quiz?

Girls		Boys
10 u		40 u
Group N	Group P	Group N	Group P
8 u	2 u	4 u	36 u

(a)
Girls : Boys
1 : 4
10 : 40

Number of girls in Group N
= 80% x 10 u
= ⁸⁰₁₀₀ x 10 u
= 8 u

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

Number of boys in Group N
= 10% x 40 u
= ¹⁰₁₀₀ x 40 u
= 4 u

Number of boys in Group P
= 40 u - 4 u
= 36 u

Group N : Group P
2 + 36 : 8 + 4 
38 : 12 _(÷2)
19 : 6

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

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

Number of sets of 4
= 90 ÷ 4
= 22 r 2

Since the number of boys in Group N is more than 90, the number of sets must be 1 more than 22.

1 u = 22 + 1 = 23

Smallest possible number of students
= 10 u + 40 u
= 50 u
= 50 x 23
= 1150

Answer(s): (a) 19 : 6; (b) 1150