PSLE
The number of boys and girls taking part in a test are in the ratio 4 : 7. These pupils are put into two groups. 60% of the boys and 30% of the girls are in Group W. The rest of the pupils are in Group X.

1. What is the ratio of the number of pupils in Group X to Group W? Give your answer in the simplest form.
2. The number of boys in Group X is fewer than 40. What is the largest possible total number of pupils taking part in the test?

Boys		Girls
40 u		70 u
Group W	Group X	Group W	Group X
24 u	16 u	21 u	49 u

(a)
Boys : Girls
4 : 7
40 : 70

Number of boys in Group W
= 60% x 40 u
= ⁶⁰₁₀₀ x 40 u
= 24 u

Number of boys in Group X
= 40 u - 24 u
= 16 u

Number of girls in Group W
= 30% x 70 u
= ³⁰₁₀₀ x 70 u
= 21 u

Number of girls in Group X
= 70 u - 21 u
= 49 u

Group X : Group W
16 + 49 : 24 + 21
65 : 45 _(÷5)
13 : 9

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

Since the number of boys in Group X 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 X is less than 40, the number of sets must be 2.

1 u = 2

Largest possible number of pupils
= 40 u + 70 u
= 110 u
= 110 x 2
= 220

Answer(s): (a) 13 : 9; (b) 220