PSLE
The number of boys and girls taking part in a quiz are in the ratio 5 : 3. These pupils are put into two groups. 50% of the boys and 10% of the girls are in Group N. The rest of the pupils are in Group P.

1. What is the ratio of the number of pupils in Group P to Group N? Give your answer in the simplest form.
2. The number of girls in Group N is more than 40. What is the smallest possible total number of pupils taking part in the quiz?

Boys		Girls
50 u		30 u
Group N	Group P	Group N	Group P
25 u	25 u	3 u	27 u

(a)
Boys : Girls
5 : 3
50 : 30

Number of boys in Group N
= 50% x 50 u
= ⁵⁰₁₀₀ x 50 u
= 25 u

Number of boys in Group P
= 50 u - 25 u
= 25 u

Number of girls in Group N
= 10% x 30 u
= ¹⁰₁₀₀ x 30 u
= 3 u

Number of girls in Group P
= 30 u - 3 u
= 27 u

Group N : Group P
25 + 27 : 25 + 3 
52 : 28 _(÷4)
13 : 7

(b)
Number of girls in Group N = 3 u

Since the number of girls in Group N is 3 u, it must be multiple of 3.

Number of sets of 3
= 40 ÷ 3
= 13 r 1

Since the number of girls in Group N is more than 40, the number of sets must be 1 more than 13.

1 u = 13 + 1 = 14

Smallest possible number of pupils
= 50 u + 30 u
= 80 u
= 80 x 14
= 1120

Answer(s): (a) 13 : 7; (b) 1120