PSLE The number of boys and girls taking part in a contest are in the ratio 1 : 6. These pupils are put into two groups. 70% of the boys and 30% of the girls are in Group L. The rest of the pupils are in Group M.
- What is the ratio of the number of pupils in Group M to Group L? Give your answer in the simplest form.
- The number of boys in Group M is fewer than 50. What is the largest possible total number of pupils taking part in the contest?
Boys |
Girls |
10 u |
60 u |
Group L |
Group M |
Group L |
Group M |
7 u |
3 u |
18 u |
42 u |
(a)
Boys : Girls
1 : 6
10 : 60
Number of boys in Group L
= 70% x 10 u
=
70100 x 10 u
= 7 u
Number of boys in Group M
= 10 u - 7 u
= 3 u
Number of girls in Group L
= 30% x 60 u
=
30100 x 60 u
= 18 u
Number of girls in Group M
= 60 u - 18 u
= 42 u
Group M : Group L
3 + 42 : 7 + 18
45 : 25
(÷5)9 : 5
(b)
Number of boys in Group M = 3 u
Since the number of boys in Group M is 3 u, it must be multiple of 3.
Number of sets of 3
= 50 ÷ 3
= 16 r 2
Since the number of boys in Group M is less than 50, the number of sets must be 16.
1 u = 16
Largest possible number of pupils
= 10 u + 60 u
= 70 u
= 70 x 16
= 1120
Answer(s): (a) 9 : 5; (b) 1120