PSLE The number of girls and boys taking part in a quiz are in the ratio 3 : 7. These pupils are put into two teams. 10% of the girls and 60% of the boys are in Team L. The rest of the pupils are in Team M.
- What is the ratio of the number of pupils in Team M to Team L? Give your answer in the simplest form.
- The number of girls in Team M is fewer than 80. What is the largest possible total number of pupils taking part in the quiz?
Girls |
Boys |
30 u |
70 u |
Team L |
Team M |
Team L |
Team M |
3 u |
27 u |
42 u |
28 u |
(a)
Girls : Boys
3 : 7
30 : 70
Number of girls in Team L
= 10% x 30 u
=
10100 x 30 u
= 3 u
Number of girls in Team M
= 30 u - 3 u
= 27 u
Number of boys in Team L
= 60% x 70 u
=
60100 x 70 u
= 42 u
Number of boys in Team M
= 70 u - 42 u
= 28 u
Team M : Team L
27 + 28 : 3 + 42
55 : 45
(÷5)11 : 9
(b)
Number of girls in Team M = 27 u
Since the number of girls in Team M is 27 u, it must be multiple of 27.
Number of sets of 27
= 80 ÷ 27
= 2 r 26
Since the number of girls in Team M is less than 80, the number of sets must be 2.
1 u = 2
Largest possible number of pupils
= 30 u + 70 u
= 100 u
= 100 x 2
= 200
Answer(s): (a) 11 : 9; (b) 200