PSLE
The number of boys and girls taking part in a contest are in the ratio 2 : 3. These pupils are put into two groups. 20% of the boys and 40% of the girls are in Group T. The rest of the pupils are in Group U.

1. What is the ratio of the number of pupils in Group U to Group T? Give your answer in the simplest form.
2. The number of boys in Group U is fewer than 50. What is the largest possible total number of pupils taking part in the contest?

Boys		Girls
20 u		30 u
Group T	Group U	Group T	Group U
4 u	16 u	12 u	18 u

(a)
Boys : Girls
2 : 3
20 : 30

Number of boys in Group T
= 20% x 20 u
= ²⁰₁₀₀ x 20 u
= 4 u

Number of boys in Group U
= 20 u - 4 u
= 16 u

Number of girls in Group T
= 40% x 30 u
= ⁴⁰₁₀₀ x 30 u
= 12 u

Number of girls in Group U
= 30 u - 12 u
= 18 u

Group U : Group T
16 + 18 : 4 + 12
34 : 16 _(÷2)
17 : 8

(b)
Number of boys in Group U = 16 u

Since the number of boys in Group U is 16 u, it must be multiple of 16.

Number of sets of 16
= 50 ÷ 16
= 3 r 2

Since the number of boys in Group U is less than 50, the number of sets must be 3.

1 u = 3

Largest possible number of pupils
= 20 u + 30 u
= 50 u
= 50 x 3
= 150

Answer(s): (a) 17 : 8; (b) 150