PSLE The number of girls and boys taking part in a test are in the ratio 3 : 8. These students are put into two groups. 40% of the girls and 30% of the boys are in Group N. The rest of the students are in Group P.
- What is the ratio of the number of students in Group P to Group N? Give your answer in the simplest form.
- The number of boys in Group N is more than 60. What is the smallest possible total number of students taking part in the test?
Girls |
Boys |
30 u |
80 u |
Group N |
Group P |
Group N |
Group P |
12 u |
18 u |
24 u |
56 u |
(a)
Girls : Boys
3 : 8
30 : 80
Number of girls in Group N
= 40% x 30 u
=
40100 x 30 u
= 12 u
Number of girls in Group P
= 30 u - 12 u
= 18 u
Number of boys in Group N
= 30% x 80 u
=
30100 x 80 u
= 24 u
Number of boys in Group P
= 80 u - 24 u
= 56 u
Group N : Group P
18 + 56 : 12 + 24
74 : 36
(÷2)37 : 18
(b)
Number of boys in Group N = 24 u
Since the number of boys in Group N is 24 u, it must be multiple of 24.
Number of sets of 24
= 60 ÷ 24
= 2 r 12
Since the number of boys in Group N is more than 60, the number of sets must be 1 more than 2.
1 u = 2 + 1 = 3
Smallest possible number of students
= 30 u + 80 u
= 110 u
= 110 x 3
= 330
Answer(s): (a) 37 : 18; (b) 330