PSLE
The number of boys and girls taking part in a test are in the ratio 5 : 2. These pupils are put into two groups. 20% of the boys and 50% 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 boys in Group W is fewer than 90. What is the largest possible total number of pupils taking part in the test?

Boys		Girls
50 u		20 u
Group V	Group W	Group V	Group W
10 u	40 u	10 u	10 u

(a)
Boys : Girls
5 : 2
50 : 20

Number of boys in Group V
= 20% x 50 u
= ²⁰₁₀₀ x 50 u
= 10 u

Number of boys in Group W
= 50 u - 10 u
= 40 u

Number of girls in Group V
= 50% x 20 u
= ⁵⁰₁₀₀ x 20 u
= 10 u

Number of girls in Group W
= 20 u - 10 u
= 10 u

Group W : Group V
40 + 10 : 10 + 10
50 : 20 _(÷10)
5 : 2

(b)
Number of boys in Group W = 40 u

Since the number of boys in Group W is 40 u, it must be multiple of 40.

Number of sets of 40
= 90 ÷ 40
= 2 r 10

Since the number of boys in Group W is less than 90, the number of sets must be 2.

1 u = 2

Largest possible number of pupils
= 50 u + 20 u
= 70 u
= 70 x 2
= 140

Answer(s): (a) 5 : 2; (b) 140