PSLE
The number of girls and boys taking part in a quiz are in the ratio 3 : 4. These pupils are put into two groups. 40% of the girls and 30% of the boys 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 boys in Group N is more than 50. What is the smallest possible total number of pupils taking part in the quiz?

Girls		Boys
30 u		40 u
Group N	Group P	Group N	Group P
12 u	18 u	12 u	28 u

(a)
Girls : Boys
3 : 4
30 : 40

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 40 u
= ³⁰₁₀₀ x 40 u
= 12 u

Number of boys in Group P
= 40 u - 12 u
= 28 u

Group N : Group P
18 + 28 : 12 + 12 
46 : 24 _(÷2)
23 : 12

(b)
Number of boys in Group N = 12 u

Since the number of boys in Group N is 12 u, it must be multiple of 12.

Number of sets of 12
= 50 ÷ 12
= 4 r 2

Since the number of boys in Group N is more than 50, the number of sets must be 1 more than 4.

1 u = 4 + 1 = 5

Smallest possible number of pupils
= 30 u + 40 u
= 70 u
= 70 x 5
= 350

Answer(s): (a) 23 : 12; (b) 350