PSLE
The number of girls and boys taking part in a test are in the ratio 7 : 8. These students are put into two groups. 40% of the girls and 20% of the boys are in Group C. The rest of the students are in Group D.

1. What is the ratio of the number of students in Group D to Group C? Give your answer in the simplest form.
2. The number of boys in Group C is more than 40. What is the smallest possible total number of students taking part in the test?

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

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

Number of girls in Group C
= 40% x 70 u
= ⁴⁰₁₀₀ x 70 u
= 28 u

Number of girls in Group D
= 70 u - 28 u
= 42 u

Number of boys in Group C
= 20% x 80 u
= ²⁰₁₀₀ x 80 u
= 16 u

Number of boys in Group D
= 80 u - 16 u
= 64 u

Group C : Group D
42 + 64 : 28 + 16 
106 : 44 _(÷2)
53 : 22

(b)
Number of boys in Group C = 16 u

Since the number of boys in Group C is 16 u, it must be multiple of 16.

Number of sets of 16
= 40 ÷ 16
= 2 r 8

Since the number of boys in Group C is more than 40, the number of sets must be 1 more than 2.

1 u = 2 + 1 = 3

Smallest possible number of students
= 70 u + 80 u
= 150 u
= 150 x 3
= 450

Answer(s): (a) 53 : 22; (b) 450