PSLE
The number of boys and girls taking part in a quiz are in the ratio 7 : 8. These pupils are put into two groups. 60% of the boys and 20% of the girls are in Group B. The rest of the pupils are in Group C.

1. What is the ratio of the number of pupils in Group C to Group B? Give your answer in the simplest form.
2. The number of girls in Group B is more than 90. What is the smallest possible total number of pupils taking part in the quiz?

Boys		Girls
70 u		80 u
Group B	Group C	Group B	Group C
42 u	28 u	16 u	64 u

(a)
Boys : Girls
7 : 8
70 : 80

Number of boys in Group B
= 60% x 70 u
= ⁶⁰₁₀₀ x 70 u
= 42 u

Number of boys in Group C
= 70 u - 42 u
= 28 u

Number of girls in Group B
= 20% x 80 u
= ²⁰₁₀₀ x 80 u
= 16 u

Number of girls in Group C
= 80 u - 16 u
= 64 u

Group B : Group C
28 + 64 : 42 + 16 
92 : 58 _(÷2)
46 : 29

(b)
Number of girls in Group B = 16 u

Since the number of girls in Group B is 16 u, it must be multiple of 16.

Number of sets of 16
= 90 ÷ 16
= 5 r 10

Since the number of girls in Group B is more than 90, the number of sets must be 1 more than 5.

1 u = 5 + 1 = 6

Smallest possible number of pupils
= 70 u + 80 u
= 150 u
= 150 x 6
= 900

Answer(s): (a) 46 : 29; (b) 900