PSLE The number of boys and girls taking part in a test are in the ratio 5 : 3. These students are put into two groups. 40% 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 girls in Group J is more than 50. What is the smallest possible total number of students taking part in the test?
Boys |
Girls |
50 u |
30 u |
Group J |
Group K |
Group J |
Group K |
20 u |
30 u |
18 u |
12 u |
(a)
Boys : Girls
5 : 3
50 : 30
Number of boys in Group J
= 40% x 50 u
=
40100 x 50 u
= 20 u
Number of boys in Group K
= 50 u - 20 u
= 30 u
Number of girls in Group J
= 60% x 30 u
=
60100 x 30 u
= 18 u
Number of girls in Group K
= 30 u - 18 u
= 12 u
Group J : Group K
30 + 12 : 20 + 18
42 : 38
(÷2)21 : 19
(b)
Number of girls in Group J = 18 u
Since the number of girls in Group J is 18 u, it must be multiple of 18.
Number of sets of 18
= 50 ÷ 18
= 2 r 14
Since the number of girls in Group J is more than 50, the number of sets must be 1 more than 2.
1 u = 2 + 1 = 3
Smallest possible number of students
= 50 u + 30 u
= 80 u
= 80 x 3
= 240
Answer(s): (a) 21 : 19; (b) 240