PSLE
The number of girls and boys taking part in a quiz are in the ratio 1 : 7. These pupils are put into two groups. 70% of the girls and 30% of the boys are in Group J. The rest of the pupils are in Group K.

1. What is the ratio of the number of pupils in Group K to Group J? Give your answer in the simplest form.
2. The number of boys in Group J is more than 60. What is the smallest possible total number of pupils taking part in the quiz?

Girls		Boys
10 u		70 u
Group J	Group K	Group J	Group K
7 u	3 u	21 u	49 u

(a)
Girls : Boys
1 : 7
10 : 70

Number of girls in Group J
= 70% x 10 u
= ⁷⁰₁₀₀ x 10 u
= 7 u

Number of girls in Group K
= 10 u - 7 u
= 3 u

Number of boys in Group J
= 30% x 70 u
= ³⁰₁₀₀ x 70 u
= 21 u

Number of boys in Group K
= 70 u - 21 u
= 49 u

Group J : Group K
3 + 49 : 7 + 21 
52 : 28 _(÷4)
13 : 7

(b)
Number of boys in Group J = 21 u

Since the number of boys in Group J is 21 u, it must be multiple of 21.

Number of sets of 21
= 60 ÷ 21
= 2 r 18

Since the number of boys in Group J is more than 60, the number of sets must be 1 more than 2.

1 u = 2 + 1 = 3

Smallest possible number of pupils
= 10 u + 70 u
= 80 u
= 80 x 3
= 240

Answer(s): (a) 13 : 7; (b) 240