PSLE
The number of girls and boys taking part in a contest are in the ratio 7 : 6. These pupils are put into two groups. 60% of the girls and 20% of the boys are in Group Q. The rest of the pupils are in Group R.

1. What is the ratio of the number of pupils in Group R to Group Q? Give your answer in the simplest form.
2. The number of boys in Group Q is more than 80. What is the smallest possible total number of pupils taking part in the contest?

Girls		Boys
70 u		60 u
Group Q	Group R	Group Q	Group R
42 u	28 u	12 u	48 u

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

Number of girls in Group Q
= 60% x 70 u
= ⁶⁰₁₀₀ x 70 u
= 42 u

Number of girls in Group R
= 70 u - 42 u
= 28 u

Number of boys in Group Q
= 20% x 60 u
= ²⁰₁₀₀ x 60 u
= 12 u

Number of boys in Group R
= 60 u - 12 u
= 48 u

Group Q : Group R
28 + 48 : 42 + 12 
76 : 54 _(÷2)
38 : 27

(b)
Number of boys in Group Q = 12 u

Since the number of boys in Group Q is 12 u, it must be multiple of 12.

Number of sets of 12
= 80 ÷ 12
= 6 r 8

Since the number of boys in Group Q is more than 80, the number of sets must be 1 more than 6.

1 u = 6 + 1 = 7

Smallest possible number of pupils
= 70 u + 60 u
= 130 u
= 130 x 7
= 910

Answer(s): (a) 38 : 27; (b) 910