PSLE
The number of girls and boys taking part in a test are in the ratio 6 : 7. These pupils are put into two groups. 80% of the girls and 20% of the boys 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 girls in Group U is fewer than 40. What is the largest possible total number of pupils taking part in the test?

Girls		Boys
60 u		70 u
Group T	Group U	Group T	Group U
48 u	12 u	14 u	56 u

(a)
Girls : Boys
6 : 7
60 : 70

Number of girls in Group T
= 80% x 60 u
= ⁸⁰₁₀₀ x 60 u
= 48 u

Number of girls in Group U
= 60 u - 48 u
= 12 u

Number of boys in Group T
= 20% x 70 u
= ²⁰₁₀₀ x 70 u
= 14 u

Number of boys in Group U
= 70 u - 14 u
= 56 u

Group U : Group T
12 + 56 : 48 + 14
68 : 62 _(÷2)
34 : 31

(b)
Number of girls in Group U = 12 u

Since the number of girls in Group U is 12 u, it must be multiple of 12.

Number of sets of 12
= 40 ÷ 12
= 3 r 4

Since the number of girls in Group U is less than 40, the number of sets must be 3.

1 u = 3

Largest possible number of pupils
= 60 u + 70 u
= 130 u
= 130 x 3
= 390

Answer(s): (a) 34 : 31; (b) 390