PSLE The number of boys and girls taking part in a quiz are in the ratio 1 : 7. These pupils are put into two teams. 10% of the boys and 30% of the girls are in Team K. The rest of the pupils are in Team L.
- What is the ratio of the number of pupils in Team L to Team K? Give your answer in the simplest form.
- The number of boys in Team L is fewer than 30. What is the largest possible total number of pupils taking part in the quiz?
Boys |
Girls |
10 u |
70 u |
Team K |
Team L |
Team K |
Team L |
1 u |
9 u |
21 u |
49 u |
(a)
Boys : Girls
1 : 7
10 : 70
Number of boys in Team K
= 10% x 10 u
=
10100 x 10 u
= 1 u
Number of boys in Team L
= 10 u - 1 u
= 9 u
Number of girls in Team K
= 30% x 70 u
=
30100 x 70 u
= 21 u
Number of girls in Team L
= 70 u - 21 u
= 49 u
Team L : Team K
9 + 49 : 1 + 21
58 : 22
(÷2)29 : 11
(b)
Number of boys in Team L = 9 u
Since the number of boys in Team L is 9 u, it must be multiple of 9.
Number of sets of 9
= 30 ÷ 9
= 3 r 3
Since the number of boys in Team L is less than 30, the number of sets must be 3.
1 u = 3
Largest possible number of pupils
= 10 u + 70 u
= 80 u
= 80 x 3
= 240
Answer(s): (a) 29 : 11; (b) 240