PSLE
The number of boys and girls taking part in a quiz are in the ratio 2 : 7. These pupils are put into two teams. 70% of the boys and 40% of the girls are in Team V. The rest of the pupils are in Team W.

1. What is the ratio of the number of pupils in Team W to Team V? Give your answer in the simplest form.
2. The number of boys in Team W is fewer than 80. What is the largest possible total number of pupils taking part in the quiz?

Boys		Girls
20 u		70 u
Team V	Team W	Team V	Team W
14 u	6 u	28 u	42 u

(a)
Boys : Girls
2 : 7
20 : 70

Number of boys in Team V
= 70% x 20 u
= ⁷⁰₁₀₀ x 20 u
= 14 u

Number of boys in Team W
= 20 u - 14 u
= 6 u

Number of girls in Team V
= 40% x 70 u
= ⁴⁰₁₀₀ x 70 u
= 28 u

Number of girls in Team W
= 70 u - 28 u
= 42 u

Team W : Team V
6 + 42 : 14 + 28
48 : 42 _(÷6)
8 : 7

(b)
Number of boys in Team W = 6 u

Since the number of boys in Team W is 6 u, it must be multiple of 6.

Number of sets of 6
= 80 ÷ 6
= 13 r 2

Since the number of boys in Team W is less than 80, the number of sets must be 13.

1 u = 13

Largest possible number of pupils
= 20 u + 70 u
= 90 u
= 90 x 13
= 1170

Answer(s): (a) 8 : 7; (b) 1170