PSLE
The number of boys and girls taking part in a test are in the ratio 3 : 4. These students are put into two groups. 60% of the boys and 10% of the girls are in Group W. The rest of the students are in Group X.

1. What is the ratio of the number of students in Group X to Group W? Give your answer in the simplest form.
2. The number of boys in Group X is fewer than 90. What is the largest possible total number of students taking part in the test?

Boys		Girls
30 u		40 u
Group W	Group X	Group W	Group X
18 u	12 u	4 u	36 u

(a)
Boys : Girls
3 : 4
30 : 40

Number of boys in Group W
= 60% x 30 u
= ⁶⁰₁₀₀ x 30 u
= 18 u

Number of boys in Group X
= 30 u - 18 u
= 12 u

Number of girls in Group W
= 10% x 40 u
= ¹⁰₁₀₀ x 40 u
= 4 u

Number of girls in Group X
= 40 u - 4 u
= 36 u

Group X : Group W
12 + 36 : 18 + 4
48 : 22 _(÷2)
24 : 11

(b)
Number of boys in Group X = 12 u

Since the number of boys in Group X is 12 u, it must be multiple of 12.

Number of sets of 12
= 90 ÷ 12
= 7 r 6

Since the number of boys in Group X is less than 90, the number of sets must be 7.

1 u = 7

Largest possible number of students
= 30 u + 40 u
= 70 u
= 70 x 7
= 490

Answer(s): (a) 24 : 11; (b) 490