PSLE
The number of girls and boys taking part in a contest are in the ratio 1 : 2. These students are put into two groups. 60% of the girls and 30% of the boys are in Group U. The rest of the students are in Group V.

1. What is the ratio of the number of students in Group V to Group U? Give your answer in the simplest form.
2. The number of boys in Group U is more than 70. What is the smallest possible total number of students taking part in the contest?

Girls		Boys
10 u		20 u
Group U	Group V	Group U	Group V
6 u	4 u	6 u	14 u

(a)
Girls : Boys
1 : 2
10 : 20

Number of girls in Group U
= 60% x 10 u
= ⁶⁰₁₀₀ x 10 u
= 6 u

Number of girls in Group V
= 10 u - 6 u
= 4 u

Number of boys in Group U
= 30% x 20 u
= ³⁰₁₀₀ x 20 u
= 6 u

Number of boys in Group V
= 20 u - 6 u
= 14 u

Group U : Group V
4 + 14 : 6 + 6 
18 : 12 _(÷6)
3 : 2

(b)
Number of boys in Group U = 6 u

Since the number of boys in Group U is 6 u, it must be multiple of 6.

Number of sets of 6
= 70 ÷ 6
= 11 r 4

Since the number of boys in Group U is more than 70, the number of sets must be 1 more than 11.

1 u = 11 + 1 = 12

Smallest possible number of students
= 10 u + 20 u
= 30 u
= 30 x 12
= 360

Answer(s): (a) 3 : 2; (b) 360