PSLE The number of boys and girls taking part in a test are in the ratio 5 : 6. These students are put into two groups. 40% of the boys and 20% 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 70. What is the largest possible total number of students taking part in the test?
Boys |
Girls |
50 u |
60 u |
Group W |
Group X |
Group W |
Group X |
20 u |
30 u |
12 u |
48 u |
(a)
Boys : Girls
5 : 6
50 : 60
Number of boys in Group W
= 40% x 50 u
=
40100 x 50 u
= 20 u
Number of boys in Group X
= 50 u - 20 u
= 30 u
Number of girls in Group W
= 20% x 60 u
=
20100 x 60 u
= 12 u
Number of girls in Group X
= 60 u - 12 u
= 48 u
Group X : Group W
30 + 48 : 20 + 12
78 : 32
(÷2)39 : 16
(b)
Number of boys in Group X = 30 u
Since the number of boys in Group X is 30 u, it must be multiple of 30.
Number of sets of 30
= 70 ÷ 30
= 2 r 10
Since the number of boys in Group X is less than 70, the number of sets must be 2.
1 u = 2
Largest possible number of students
= 50 u + 60 u
= 110 u
= 110 x 2
= 220
Answer(s): (a) 39 : 16; (b) 220