PSLE
The number of girls and boys taking part in a contest are in the ratio 7 : 8. These pupils are put into two groups. 70% of the girls and 10% of the boys are in Group B. The rest of the pupils are in Group C.

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

Girls		Boys
70 u		80 u
Group B	Group C	Group B	Group C
49 u	21 u	8 u	72 u

(a)
Girls : Boys
7 : 8
70 : 80

Number of girls in Group B
= 70% x 70 u
= ⁷⁰₁₀₀ x 70 u
= 49 u

Number of girls in Group C
= 70 u - 49 u
= 21 u

Number of boys in Group B
= 10% x 80 u
= ¹⁰₁₀₀ x 80 u
= 8 u

Number of boys in Group C
= 80 u - 8 u
= 72 u

Group B : Group C
21 + 72 : 49 + 8 
93 : 57 _(÷3)
31 : 19

(b)
Number of boys in Group B = 8 u

Since the number of boys in Group B is 8 u, it must be multiple of 8.

Number of sets of 8
= 60 ÷ 8
= 7 r 4

Since the number of boys in Group B is more than 60, the number of sets must be 1 more than 7.

1 u = 7 + 1 = 8

Smallest possible number of pupils
= 70 u + 80 u
= 150 u
= 150 x 8
= 1200

Answer(s): (a) 31 : 19; (b) 1200