PSLE The number of girls and boys taking part in a quiz are in the ratio 5 : 8. These students are put into two groups. 20% of the girls and 30% of the boys are in Group T. The rest of the students are in Group U.
- What is the ratio of the number of students in Group U to Group T? Give your answer in the simplest form.
- The number of boys in Group T is more than 80. What is the smallest possible total number of students taking part in the quiz?
Girls |
Boys |
50 u |
80 u |
Group T |
Group U |
Group T |
Group U |
10 u |
40 u |
24 u |
56 u |
(a)
Girls : Boys
5 : 8
50 : 80
Number of girls in Group T
= 20% x 50 u
=
20100 x 50 u
= 10 u
Number of girls in Group U
= 50 u - 10 u
= 40 u
Number of boys in Group T
= 30% x 80 u
=
30100 x 80 u
= 24 u
Number of boys in Group U
= 80 u - 24 u
= 56 u
Group T : Group U
40 + 56 : 10 + 24
96 : 34
(÷2)48 : 17
(b)
Number of boys in Group T = 24 u
Since the number of boys in Group T 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 T 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 + 80 u
= 130 u
= 130 x 4
= 520
Answer(s): (a) 48 : 17; (b) 520