PSLE
The number of boys and girls taking part in a quiz are in the ratio 2 : 5. These students are put into two teams. 30% of the boys and 40% of the girls are in Team X. The rest of the students are in Team Y.

1. What is the ratio of the number of students in Team Y to Team X? Give your answer in the simplest form.
2. The number of boys in Team Y is fewer than 60. What is the largest possible total number of students taking part in the quiz?

Boys		Girls
20 u		50 u
Team X	Team Y	Team X	Team Y
6 u	14 u	20 u	30 u

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

Number of boys in Team X
= 30% x 20 u
= ³⁰₁₀₀ x 20 u
= 6 u

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

Number of girls in Team X
= 40% x 50 u
= ⁴⁰₁₀₀ x 50 u
= 20 u

Number of girls in Team Y
= 50 u - 20 u
= 30 u

Team Y : Team X
14 + 30 : 6 + 20
44 : 26 _(÷2)
22 : 13

(b)
Number of boys in Team Y = 14 u

Since the number of boys in Team Y is 14 u, it must be multiple of 14.

Number of sets of 14
= 60 ÷ 14
= 4 r 4

Since the number of boys in Team Y is less than 60, the number of sets must be 4.

1 u = 4

Largest possible number of students
= 20 u + 50 u
= 70 u
= 70 x 4
= 280

Answer(s): (a) 22 : 13; (b) 280