PSLE The number of girls and boys taking part in a quiz are in the ratio 5 : 6. These students are put into two groups. 20% 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 boys in Group V is more than 80. What is the smallest possible total number of students taking part in the quiz?
Girls |
Boys |
50 u |
60 u |
Group V |
Group W |
Group V |
Group W |
10 u |
40 u |
24 u |
36 u |
(a)
Girls : Boys
5 : 6
50 : 60
Number of girls in Group V
= 20% x 50 u
=
20100 x 50 u
= 10 u
Number of girls in Group W
= 50 u - 10 u
= 40 u
Number of boys in Group V
= 40% x 60 u
=
40100 x 60 u
= 24 u
Number of boys in Group W
= 60 u - 24 u
= 36 u
Group V : Group W
40 + 36 : 10 + 24
76 : 34
(÷2)38 : 17
(b)
Number of boys in Group V = 24 u
Since the number of boys in Group V is 24 u, it must be multiple of 24.
Number of sets of 24
= 80 ÷ 24
= 3 r 8
Since the number of boys in Group V is more than 80, the number of sets must be 1 more than 3.
1 u = 3 + 1 = 4
Smallest possible number of students
= 50 u + 60 u
= 110 u
= 110 x 4
= 440
Answer(s): (a) 38 : 17; (b) 440