PSLE The number of girls and boys taking part in a test are in the ratio 1 : 6. These students are put into two groups. 10% of the girls and 40% of the boys 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 girls in Group X is fewer than 50. What is the largest possible total number of students taking part in the test?
Girls |
Boys |
10 u |
60 u |
Group W |
Group X |
Group W |
Group X |
1 u |
9 u |
24 u |
36 u |
(a)
Girls : Boys
1 : 6
10 : 60
Number of girls in Group W
= 10% x 10 u
=
10100 x 10 u
= 1 u
Number of girls in Group X
= 10 u - 1 u
= 9 u
Number of boys in Group W
= 40% x 60 u
=
40100 x 60 u
= 24 u
Number of boys in Group X
= 60 u - 24 u
= 36 u
Group X : Group W
9 + 36 : 1 + 24
45 : 25
(÷5)9 : 5
(b)
Number of girls in Group X = 9 u
Since the number of girls in Group X is 9 u, it must be multiple of 9.
Number of sets of 9
= 50 ÷ 9
= 5 r 5
Since the number of girls in Group X is less than 50, the number of sets must be 5.
1 u = 5
Largest possible number of students
= 10 u + 60 u
= 70 u
= 70 x 5
= 350
Answer(s): (a) 9 : 5; (b) 350