PSLE
The number of girls and boys taking part in a quiz are in the ratio 5 : 7. These pupils are put into two groups. 10% of the girls and 40% of the boys 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 W is more than 80. What is the smallest possible total number of pupils taking part in the quiz?

Girls		Boys
50 u		70 u
Group W	Group X	Group W	Group X
5 u	45 u	28 u	42 u

(a)
Girls : Boys
5 : 7
50 : 70

Number of girls in Group W
= 10% x 50 u
= ¹⁰₁₀₀ x 50 u
= 5 u

Number of girls in Group X
= 50 u - 5 u
= 45 u

Number of boys in Group W
= 40% x 70 u
= ⁴⁰₁₀₀ x 70 u
= 28 u

Number of boys in Group X
= 70 u - 28 u
= 42 u

Group W : Group X
45 + 42 : 5 + 28 
87 : 33 _(÷3)
29 : 11

(b)
Number of boys in Group W = 28 u

Since the number of boys in Group W is 28 u, it must be multiple of 28.

Number of sets of 28
= 80 ÷ 28
= 2 r 24

Since the number of boys in Group W is more than 80, the number of sets must be 1 more than 2.

1 u = 2 + 1 = 3

Smallest possible number of pupils
= 50 u + 70 u
= 120 u
= 120 x 3
= 360

Answer(s): (a) 29 : 11; (b) 360