PSLE
The number of girls and boys taking part in a test are in the ratio 7 : 3. These pupils are put into two groups. 40% of the girls and 20% of the boys are in Group P. The rest of the pupils are in Group Q.

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

Girls		Boys
70 u		30 u
Group P	Group Q	Group P	Group Q
28 u	42 u	6 u	24 u

(a)
Girls : Boys
7 : 3
70 : 30

Number of girls in Group P
= 40% x 70 u
= ⁴⁰₁₀₀ x 70 u
= 28 u

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

Number of boys in Group P
= 20% x 30 u
= ²⁰₁₀₀ x 30 u
= 6 u

Number of boys in Group Q
= 30 u - 6 u
= 24 u

Group P : Group Q
42 + 24 : 28 + 6 
66 : 34 _(÷2)
33 : 17

(b)
Number of boys in Group P = 6 u

Since the number of boys in Group P is 6 u, it must be multiple of 6.

Number of sets of 6
= 80 ÷ 6
= 13 r 2

Since the number of boys in Group P is more than 80, the number of sets must be 1 more than 13.

1 u = 13 + 1 = 14

Smallest possible number of pupils
= 70 u + 30 u
= 100 u
= 100 x 14
= 1400

Answer(s): (a) 33 : 17; (b) 1400