PSLE The number of boys and girls taking part in a test are in the ratio 3 : 7. These students are put into two groups. 10% of the boys and 60% of the girls are in Group J. The rest of the students are in Group K.
- What is the ratio of the number of students in Group K to Group J? Give your answer in the simplest form.
- The number of boys in Group K is fewer than 70. What is the largest possible total number of students taking part in the test?
Boys |
Girls |
30 u |
70 u |
Group J |
Group K |
Group J |
Group K |
3 u |
27 u |
42 u |
28 u |
(a)
Boys : Girls
3 : 7
30 : 70
Number of boys in Group J
= 10% x 30 u
=
10100 x 30 u
= 3 u
Number of boys in Group K
= 30 u - 3 u
= 27 u
Number of girls in Group J
= 60% x 70 u
=
60100 x 70 u
= 42 u
Number of girls in Group K
= 70 u - 42 u
= 28 u
Group K : Group J
27 + 28 : 3 + 42
55 : 45
(÷5)11 : 9
(b)
Number of boys in Group K = 27 u
Since the number of boys in Group K is 27 u, it must be multiple of 27.
Number of sets of 27
= 70 ÷ 27
= 2 r 16
Since the number of boys in Group K is less than 70, the number of sets must be 2.
1 u = 2
Largest possible number of students
= 30 u + 70 u
= 100 u
= 100 x 2
= 200
Answer(s): (a) 11 : 9; (b) 200