PSLE The number of girls and boys taking part in a quiz are in the ratio 1 : 3. These pupils are put into two teams. 60% of the girls and 40% of the boys are in Team T. The rest of the pupils are in Team U.
- What is the ratio of the number of pupils in Team U to Team T? Give your answer in the simplest form.
- The number of boys in Team T is more than 50. What is the smallest possible total number of pupils taking part in the quiz?
Girls |
Boys |
10 u |
30 u |
Team T |
Team U |
Team T |
Team U |
6 u |
4 u |
12 u |
18 u |
(a)
Girls : Boys
1 : 3
10 : 30
Number of girls in Team T
= 60% x 10 u
=
60100 x 10 u
= 6 u
Number of girls in Team U
= 10 u - 6 u
= 4 u
Number of boys in Team T
= 40% x 30 u
=
40100 x 30 u
= 12 u
Number of boys in Team U
= 30 u - 12 u
= 18 u
Team T : Team U
4 + 18 : 6 + 12
22 : 18
(÷2)11 : 9
(b)
Number of boys in Team T = 12 u
Since the number of boys in Team T is 12 u, it must be multiple of 12.
Number of sets of 12
= 50 ÷ 12
= 4 r 2
Since the number of boys in Team T is more than 50, the number of sets must be 1 more than 4.
1 u = 4 + 1 = 5
Smallest possible number of pupils
= 10 u + 30 u
= 40 u
= 40 x 5
= 200
Answer(s): (a) 11 : 9; (b) 200