PSLE
The number of boys and girls taking part in a contest are in the ratio 8 : 7. These students are put into two groups. 20% of the boys and 50% of the girls 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 girls in Group N is more than 90. What is the smallest possible total number of students taking part in the contest?

Boys		Girls
80 u		70 u
Group N	Group P	Group N	Group P
16 u	64 u	35 u	35 u

(a)
Boys : Girls
8 : 7
80 : 70

Number of boys in Group N
= 20% x 80 u
= ²⁰₁₀₀ x 80 u
= 16 u

Number of boys in Group P
= 80 u - 16 u
= 64 u

Number of girls in Group N
= 50% x 70 u
= ⁵⁰₁₀₀ x 70 u
= 35 u

Number of girls in Group P
= 70 u - 35 u
= 35 u

Group N : Group P
64 + 35 : 16 + 35 
99 : 51 _(÷3)
33 : 17

(b)
Number of girls in Group N = 35 u

Since the number of girls in Group N is 35 u, it must be multiple of 35.

Number of sets of 35
= 90 ÷ 35
= 2 r 20

Since the number of girls in Group N is more than 90, the number of sets must be 1 more than 2.

1 u = 2 + 1 = 3

Smallest possible number of students
= 80 u + 70 u
= 150 u
= 150 x 3
= 450

Answer(s): (a) 33 : 17; (b) 450