PSLE
The number of boys and girls taking part in a quiz are in the ratio 1 : 5. These pupils are put into two groups. 10% of the boys and 50% 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 girls in Group T is more than 70. What is the smallest possible total number of pupils taking part in the quiz?

Boys		Girls
10 u		50 u
Group T	Group U	Group T	Group U
1 u	9 u	25 u	25 u

(a)
Boys : Girls
1 : 5
10 : 50

Number of boys in Group T
= 10% x 10 u
= ¹⁰₁₀₀ x 10 u
= 1 u

Number of boys in Group U
= 10 u - 1 u
= 9 u

Number of girls in Group T
= 50% x 50 u
= ⁵⁰₁₀₀ x 50 u
= 25 u

Number of girls in Group U
= 50 u - 25 u
= 25 u

Group T : Group U
9 + 25 : 1 + 25 
34 : 26 _(÷2)
17 : 13

(b)
Number of girls in Group T = 25 u

Since the number of girls in Group T is 25 u, it must be multiple of 25.

Number of sets of 25
= 70 ÷ 25
= 2 r 20

Since the number of girls in Group T is more than 70, the number of sets must be 1 more than 2.

1 u = 2 + 1 = 3

Smallest possible number of pupils
= 10 u + 50 u
= 60 u
= 60 x 3
= 180

Answer(s): (a) 17 : 13; (b) 180