PSLE
The number of girls and boys taking part in a contest are in the ratio 1 : 5. These pupils are put into two groups. 70% 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 girls in Group P is fewer than 80. What is the largest possible total number of pupils taking part in the contest?

Girls		Boys
10 u		50 u
Group N	Group P	Group N	Group P
7 u	3 u	15 u	35 u

(a)
Girls : Boys
1 : 5
10 : 50

Number of girls in Group N
= 70% x 10 u
= ⁷⁰₁₀₀ x 10 u
= 7 u

Number of girls in Group P
= 10 u - 7 u
= 3 u

Number of boys in Group N
= 30% x 50 u
= ³⁰₁₀₀ x 50 u
= 15 u

Number of boys in Group P
= 50 u - 15 u
= 35 u

Group P : Group N
3 + 35 : 7 + 15
38 : 22 _(÷2)
19 : 11

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

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

Number of sets of 3
= 80 ÷ 3
= 26 r 2

Since the number of girls in Group P is less than 80, the number of sets must be 26.

1 u = 26

Largest possible number of pupils
= 10 u + 50 u
= 60 u
= 60 x 26
= 1560

Answer(s): (a) 19 : 11; (b) 1560