PSLE The number of girls and boys taking part in a test are in the ratio 1 : 2. These pupils are put into two teams. 10% of the girls and 20% of the boys are in Team E. The rest of the pupils are in Team F.
- What is the ratio of the number of pupils in Team F to Team E? Give your answer in the simplest form.
- The number of girls in Team F is fewer than 50. What is the largest possible total number of pupils taking part in the test?
Girls |
Boys |
10 u |
20 u |
Team E |
Team F |
Team E |
Team F |
1 u |
9 u |
4 u |
16 u |
(a)
Girls : Boys
1 : 2
10 : 20
Number of girls in Team E
= 10% x 10 u
=
10100 x 10 u
= 1 u
Number of girls in Team F
= 10 u - 1 u
= 9 u
Number of boys in Team E
= 20% x 20 u
=
20100 x 20 u
= 4 u
Number of boys in Team F
= 20 u - 4 u
= 16 u
Team F : Team E
9 + 16 : 1 + 4
25 : 5
(÷5)5 : 1
(b)
Number of girls in Team F = 9 u
Since the number of girls in Team F is 9 u, it must be multiple of 9.
Number of sets of 9
= 50 ÷ 9
= 5 r 5
Since the number of girls in Team F is less than 50, the number of sets must be 5.
1 u = 5
Largest possible number of pupils
= 10 u + 20 u
= 30 u
= 30 x 5
= 150
Answer(s): (a) 5 : 1; (b) 150