PSLE
The number of girls and boys taking part in a contest are in the ratio 8 : 7. These students are put into two groups. 60% of the girls and 10% of the boys are in Group X. The rest of the students are in Group Y.

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

Girls		Boys
80 u		70 u
Group X	Group Y	Group X	Group Y
48 u	32 u	7 u	63 u

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

Number of girls in Group X
= 60% x 80 u
= ⁶⁰₁₀₀ x 80 u
= 48 u

Number of girls in Group Y
= 80 u - 48 u
= 32 u

Number of boys in Group X
= 10% x 70 u
= ¹⁰₁₀₀ x 70 u
= 7 u

Number of boys in Group Y
= 70 u - 7 u
= 63 u

Group X : Group Y
32 + 63 : 48 + 7 
95 : 55 _(÷5)
19 : 11

(b)
Number of boys in Group X = 7 u

Since the number of boys in Group X is 7 u, it must be multiple of 7.

Number of sets of 7
= 90 ÷ 7
= 12 r 6

Since the number of boys in Group X is more than 90, the number of sets must be 1 more than 12.

1 u = 12 + 1 = 13

Smallest possible number of students
= 80 u + 70 u
= 150 u
= 150 x 13
= 1950

Answer(s): (a) 19 : 11; (b) 1950