PSLE
The number of girls and boys taking part in a test are in the ratio 1 : 8. These pupils are put into two groups. 70% of the girls and 10% of the boys are in Group Y. The rest of the pupils are in Group Z.

1. What is the ratio of the number of pupils in Group Z to Group Y? Give your answer in the simplest form.
2. The number of girls in Group Z is fewer than 80. What is the largest possible total number of pupils taking part in the test?

Girls		Boys
10 u		80 u
Group Y	Group Z	Group Y	Group Z
7 u	3 u	8 u	72 u

(a)
Girls : Boys
1 : 8
10 : 80

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

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

Number of boys in Group Y
= 10% x 80 u
= ¹⁰₁₀₀ x 80 u
= 8 u

Number of boys in Group Z
= 80 u - 8 u
= 72 u

Group Z : Group Y
3 + 72 : 7 + 8
75 : 15 _(÷15)
5 : 1

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

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

1 u = 26

Largest possible number of pupils
= 10 u + 80 u
= 90 u
= 90 x 26
= 2340

Answer(s): (a) 5 : 1; (b) 2340