PSLE The number of boys and girls taking part in a quiz are in the ratio 2 : 7. These pupils are put into two teams. 10% of the boys and 40% of the girls are in Team Q. The rest of the pupils are in Team R.
- What is the ratio of the number of pupils in Team R to Team Q? Give your answer in the simplest form.
- The number of girls in Team Q is more than 90. What is the smallest possible total number of pupils taking part in the quiz?
Boys |
Girls |
20 u |
70 u |
Team Q |
Team R |
Team Q |
Team R |
2 u |
18 u |
28 u |
42 u |
(a)
Boys : Girls
2 : 7
20 : 70
Number of boys in Team Q
= 10% x 20 u
=
10100 x 20 u
= 2 u
Number of boys in Team R
= 20 u - 2 u
= 18 u
Number of girls in Team Q
= 40% x 70 u
=
40100 x 70 u
= 28 u
Number of girls in Team R
= 70 u - 28 u
= 42 u
Team Q : Team R
18 + 42 : 2 + 28
60 : 30
(÷30)2 : 1
(b)
Number of girls in Team Q = 28 u
Since the number of girls in Team Q is 28 u, it must be multiple of 28.
Number of sets of 28
= 90 ÷ 28
= 3 r 6
Since the number of girls in Team Q is more than 90, the number of sets must be 1 more than 3.
1 u = 3 + 1 = 4
Smallest possible number of pupils
= 20 u + 70 u
= 90 u
= 90 x 4
= 360
Answer(s): (a) 2 : 1; (b) 360