PSLE
The number of girls and boys taking part in a test are in the ratio 5 : 7. These students are put into two groups. 40% of the girls and 20% of the boys are in Group Y. The rest of the students are in Group Z.

1. What is the ratio of the number of students in Group Z to Group Y? Give your answer in the simplest form.
2. The number of boys in Group Y is more than 90. What is the smallest possible total number of students taking part in the test?

Girls		Boys
50 u		70 u
Group Y	Group Z	Group Y	Group Z
20 u	30 u	14 u	56 u

(a)
Girls : Boys
5 : 7
50 : 70

Number of girls in Group Y
= 40% x 50 u
= ⁴⁰₁₀₀ x 50 u
= 20 u

Number of girls in Group Z
= 50 u - 20 u
= 30 u

Number of boys in Group Y
= 20% x 70 u
= ²⁰₁₀₀ x 70 u
= 14 u

Number of boys in Group Z
= 70 u - 14 u
= 56 u

Group Y : Group Z
30 + 56 : 20 + 14 
86 : 34 _(÷2)
43 : 17

(b)
Number of boys in Group Y = 14 u

Since the number of boys in Group Y is 14 u, it must be multiple of 14.

Number of sets of 14
= 90 ÷ 14
= 6 r 6

Since the number of boys in Group Y is more than 90, the number of sets must be 1 more than 6.

1 u = 6 + 1 = 7

Smallest possible number of students
= 50 u + 70 u
= 120 u
= 120 x 7
= 840

Answer(s): (a) 43 : 17; (b) 840