PSLE
The number of girls and boys taking part in a contest are in the ratio 4 : 5. These pupils are put into two groups. 60% of the girls and 40% of the boys are in Group E. The rest of the pupils are in Group F.

1. What is the ratio of the number of pupils in Group F to Group E? Give your answer in the simplest form.
2. The number of girls in Group F is fewer than 40. What is the largest possible total number of pupils taking part in the contest?

Girls		Boys
40 u		50 u
Group E	Group F	Group E	Group F
24 u	16 u	20 u	30 u

(a)
Girls : Boys
4 : 5
40 : 50

Number of girls in Group E
= 60% x 40 u
= ⁶⁰₁₀₀ x 40 u
= 24 u

Number of girls in Group F
= 40 u - 24 u
= 16 u

Number of boys in Group E
= 40% x 50 u
= ⁴⁰₁₀₀ x 50 u
= 20 u

Number of boys in Group F
= 50 u - 20 u
= 30 u

Group F : Group E
16 + 30 : 24 + 20
46 : 44 _(÷2)
23 : 22

(b)
Number of girls in Group F = 16 u

Since the number of girls in Group F is 16 u, it must be multiple of 16.

Number of sets of 16
= 40 ÷ 16
= 2 r 8

Since the number of girls in Group F is less than 40, the number of sets must be 2.

1 u = 2

Largest possible number of pupils
= 40 u + 50 u
= 90 u
= 90 x 2
= 180

Answer(s): (a) 23 : 22; (b) 180