PSLE The number of girls and boys taking part in a contest are in the ratio 5 : 8. These students are put into two groups. 60% of the girls and 40% of the boys are in Group V. The rest of the students are in Group W.
- What is the ratio of the number of students in Group W to Group V? Give your answer in the simplest form.
- The number of girls in Group W is fewer than 50. What is the largest possible total number of students taking part in the contest?
Girls |
Boys |
50 u |
80 u |
Group V |
Group W |
Group V |
Group W |
30 u |
20 u |
32 u |
48 u |
(a)
Girls : Boys
5 : 8
50 : 80
Number of girls in Group V
= 60% x 50 u
=
60100 x 50 u
= 30 u
Number of girls in Group W
= 50 u - 30 u
= 20 u
Number of boys in Group V
= 40% x 80 u
=
40100 x 80 u
= 32 u
Number of boys in Group W
= 80 u - 32 u
= 48 u
Group W : Group V
20 + 48 : 30 + 32
68 : 62
(÷2)34 : 31
(b)
Number of girls in Group W = 20 u
Since the number of girls in Group W is 20 u, it must be multiple of 20.
Number of sets of 20
= 50 ÷ 20
= 2 r 10
Since the number of girls in Group W is less than 50, the number of sets must be 2.
1 u = 2
Largest possible number of students
= 50 u + 80 u
= 130 u
= 130 x 2
= 260
Answer(s): (a) 34 : 31; (b) 260