PSLE
The number of girls and boys taking part in a test are in the ratio 1 : 6. These pupils are put into two groups. 40% of the girls and 50% 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 girls in Group Q is fewer than 80. What is the largest possible total number of pupils taking part in the test?

Girls		Boys
10 u		60 u
Group P	Group Q	Group P	Group Q
4 u	6 u	30 u	30 u

(a)
Girls : Boys
1 : 6
10 : 60

Number of girls in Group P
= 40% x 10 u
= ⁴⁰₁₀₀ x 10 u
= 4 u

Number of girls in Group Q
= 10 u - 4 u
= 6 u

Number of boys in Group P
= 50% x 60 u
= ⁵⁰₁₀₀ x 60 u
= 30 u

Number of boys in Group Q
= 60 u - 30 u
= 30 u

Group Q : Group P
6 + 30 : 4 + 30
36 : 34 _(÷2)
18 : 17

(b)
Number of girls in Group Q = 6 u

Since the number of girls in Group Q is 6 u, it must be multiple of 6.

Number of sets of 6
= 80 ÷ 6
= 13 r 2

Since the number of girls in Group Q is less than 80, the number of sets must be 13.

1 u = 13

Largest possible number of pupils
= 10 u + 60 u
= 70 u
= 70 x 13
= 910

Answer(s): (a) 18 : 17; (b) 910