PSLE
The number of girls and boys taking part in a test are in the ratio 5 : 7. These pupils are put into two teams. 60% of the girls and 40% of the boys are in Team T. The rest of the pupils are in Team U.

1. What is the ratio of the number of pupils in Team U to Team T? Give your answer in the simplest form.
2. The number of boys in Team T is more than 80. What is the smallest possible total number of pupils taking part in the test?

Girls		Boys
50 u		70 u
Team T	Team U	Team T	Team U
30 u	20 u	28 u	42 u

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

Number of girls in Team T
= 60% x 50 u
= ⁶⁰₁₀₀ x 50 u
= 30 u

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

Number of boys in Team T
= 40% x 70 u
= ⁴⁰₁₀₀ x 70 u
= 28 u

Number of boys in Team U
= 70 u - 28 u
= 42 u

Team T : Team U
20 + 42 : 30 + 28 
62 : 58 _(÷2)
31 : 29

(b)
Number of boys in Team T = 28 u

Since the number of boys in Team T 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 Team T 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) 31 : 29; (b) 360