PSLE
The number of boys and girls taking part in a contest are in the ratio 4 : 7. These pupils are put into two teams. 10% of the boys and 30% of the girls 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 girls in Team T is more than 90. What is the smallest possible total number of pupils taking part in the contest?

Boys		Girls
40 u		70 u
Team T	Team U	Team T	Team U
4 u	36 u	21 u	49 u

(a)
Boys : Girls
4 : 7
40 : 70

Number of boys in Team T
= 10% x 40 u
= ¹⁰₁₀₀ x 40 u
= 4 u

Number of boys in Team U
= 40 u - 4 u
= 36 u

Number of girls in Team T
= 30% x 70 u
= ³⁰₁₀₀ x 70 u
= 21 u

Number of girls in Team U
= 70 u - 21 u
= 49 u

Team T : Team U
36 + 49 : 4 + 21 
85 : 25 _(÷5)
17 : 5

(b)
Number of girls in Team T = 21 u

Since the number of girls in Team T is 21 u, it must be multiple of 21.

Number of sets of 21
= 90 ÷ 21
= 4 r 6

Since the number of girls in Team T is more than 90, the number of sets must be 1 more than 4.

1 u = 4 + 1 = 5

Smallest possible number of pupils
= 40 u + 70 u
= 110 u
= 110 x 5
= 550

Answer(s): (a) 17 : 5; (b) 550