PSLE
The number of boys and girls taking part in a quiz are in the ratio 3 : 2. These pupils are put into two groups. 20% of the boys and 60% of the girls are in Group P. The rest of the pupils are in Group Q.

1. What is the ratio of the number of pupils in Group Q to Group P? Give your answer in the simplest form.
2. The number of boys in Group Q is fewer than 90. What is the largest possible total number of pupils taking part in the quiz?

Boys		Girls
30 u		20 u
Group P	Group Q	Group P	Group Q
6 u	24 u	12 u	8 u

(a)
Boys : Girls
3 : 2
30 : 20

Number of boys in Group P
= 20% x 30 u
= ²⁰₁₀₀ x 30 u
= 6 u

Number of boys in Group Q
= 30 u - 6 u
= 24 u

Number of girls in Group P
= 60% x 20 u
= ⁶⁰₁₀₀ x 20 u
= 12 u

Number of girls in Group Q
= 20 u - 12 u
= 8 u

Group Q : Group P
24 + 8 : 6 + 12
32 : 18 _(÷2)
16 : 9

(b)
Number of boys in Group Q = 24 u

Since the number of boys in Group Q is 24 u, it must be multiple of 24.

Number of sets of 24
= 90 ÷ 24
= 3 r 18

Since the number of boys in Group Q is less than 90, the number of sets must be 3.

1 u = 3

Largest possible number of pupils
= 30 u + 20 u
= 50 u
= 50 x 3
= 150

Answer(s): (a) 16 : 9; (b) 150