PSLE
The number of boys and girls taking part in a test are in the ratio 5 : 6. These pupils are put into two groups. 60% of the boys and 30% of the girls are in Group V. The rest of the pupils are in Group W.

1. What is the ratio of the number of pupils in Group W to Group V? Give your answer in the simplest form.
2. The number of girls in Group V is more than 80. What is the smallest possible total number of pupils taking part in the test?

Boys		Girls
50 u		60 u
Group V	Group W	Group V	Group W
30 u	20 u	18 u	42 u

(a)
Boys : Girls
5 : 6
50 : 60

Number of boys in Group V
= 60% x 50 u
= ⁶⁰₁₀₀ x 50 u
= 30 u

Number of boys in Group W
= 50 u - 30 u
= 20 u

Number of girls in Group V
= 30% x 60 u
= ³⁰₁₀₀ x 60 u
= 18 u

Number of girls in Group W
= 60 u - 18 u
= 42 u

Group V : Group W
20 + 42 : 30 + 18 
62 : 48 _(÷2)
31 : 24

(b)
Number of girls in Group V = 18 u

Since the number of girls in Group V is 18 u, it must be multiple of 18.

Number of sets of 18
= 80 ÷ 18
= 4 r 8

Since the number of girls in Group V is more than 80, the number of sets must be 1 more than 4.

1 u = 4 + 1 = 5

Smallest possible number of pupils
= 50 u + 60 u
= 110 u
= 110 x 5
= 550

Answer(s): (a) 31 : 24; (b) 550