PSLE
The number of boys and girls taking part in a contest are in the ratio 7 : 3. These pupils are put into two groups. 50% of the boys and 10% of the girls are in Group K. The rest of the pupils are in Group L.

1. What is the ratio of the number of pupils in Group L to Group K? Give your answer in the simplest form.
2. The number of boys in Group L is fewer than 80. What is the largest possible total number of pupils taking part in the contest?

Boys		Girls
70 u		30 u
Group K	Group L	Group K	Group L
35 u	35 u	3 u	27 u

(a)
Boys : Girls
7 : 3
70 : 30

Number of boys in Group K
= 50% x 70 u
= ⁵⁰₁₀₀ x 70 u
= 35 u

Number of boys in Group L
= 70 u - 35 u
= 35 u

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

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

Group L : Group K
35 + 27 : 35 + 3
62 : 38 _(÷2)
31 : 19

(b)
Number of boys in Group L = 35 u

Since the number of boys in Group L is 35 u, it must be multiple of 35.

Number of sets of 35
= 80 ÷ 35
= 2 r 10

Since the number of boys in Group L is less than 80, the number of sets must be 2.

1 u = 2

Largest possible number of pupils
= 70 u + 30 u
= 100 u
= 100 x 2
= 200

Answer(s): (a) 31 : 19; (b) 200