PSLE
The number of boys and girls taking part in a contest are in the ratio 1 : 6. These pupils are put into two groups. 10% of the boys and 40% of the girls are in Group M. The rest of the pupils are in Group N.

1. What is the ratio of the number of pupils in Group N to Group M? Give your answer in the simplest form.
2. The number of girls in Group M is more than 80. What is the smallest possible total number of pupils taking part in the contest?

Boys		Girls
10 u		60 u
Group M	Group N	Group M	Group N
1 u	9 u	24 u	36 u

(a)
Boys : Girls
1 : 6
10 : 60

Number of boys in Group M
= 10% x 10 u
= ¹⁰₁₀₀ x 10 u
= 1 u

Number of boys in Group N
= 10 u - 1 u
= 9 u

Number of girls in Group M
= 40% x 60 u
= ⁴⁰₁₀₀ x 60 u
= 24 u

Number of girls in Group N
= 60 u - 24 u
= 36 u

Group M : Group N
9 + 36 : 1 + 24 
45 : 25 _(÷5)
9 : 5

(b)
Number of girls in Group M = 24 u

Since the number of girls in Group M is 24 u, it must be multiple of 24.

Number of sets of 24
= 80 ÷ 24
= 3 r 8

Since the number of girls in Group M is more than 80, the number of sets must be 1 more than 3.

1 u = 3 + 1 = 4

Smallest possible number of pupils
= 10 u + 60 u
= 70 u
= 70 x 4
= 280

Answer(s): (a) 9 : 5; (b) 280