PSLE The number of boys and girls taking part in a contest are in the ratio 6 : 5. These students are put into two groups. 30% of the boys and 60% of the girls are in Group W. The rest of the students are in Group X.
- What is the ratio of the number of students in Group X to Group W? Give your answer in the simplest form.
- The number of boys in Group X is fewer than 90. What is the largest possible total number of students taking part in the contest?
Boys |
Girls |
60 u |
50 u |
Group W |
Group X |
Group W |
Group X |
18 u |
42 u |
30 u |
20 u |
(a)
Boys : Girls
6 : 5
60 : 50
Number of boys in Group W
= 30% x 60 u
=
30100 x 60 u
= 18 u
Number of boys in Group X
= 60 u - 18 u
= 42 u
Number of girls in Group W
= 60% x 50 u
=
60100 x 50 u
= 30 u
Number of girls in Group X
= 50 u - 30 u
= 20 u
Group X : Group W
42 + 20 : 18 + 30
62 : 48
(÷2)31 : 24
(b)
Number of boys in Group X = 42 u
Since the number of boys in Group X is 42 u, it must be multiple of 42.
Number of sets of 42
= 90 ÷ 42
= 2 r 6
Since the number of boys in Group X is less than 90, the number of sets must be 2.
1 u = 2
Largest possible number of students
= 60 u + 50 u
= 110 u
= 110 x 2
= 220
Answer(s): (a) 31 : 24; (b) 220