PSLE The number of girls and boys taking part in a test are in the ratio 6 : 7. These students are put into two groups. 10% of the girls and 20% of the boys are in Group U. The rest of the students are in Group V.
- What is the ratio of the number of students in Group V to Group U? Give your answer in the simplest form.
- The number of boys in Group U is more than 30. What is the smallest possible total number of students taking part in the test?
Girls |
Boys |
60 u |
70 u |
Group U |
Group V |
Group U |
Group V |
6 u |
54 u |
14 u |
56 u |
(a)
Girls : Boys
6 : 7
60 : 70
Number of girls in Group U
= 10% x 60 u
=
10100 x 60 u
= 6 u
Number of girls in Group V
= 60 u - 6 u
= 54 u
Number of boys in Group U
= 20% x 70 u
=
20100 x 70 u
= 14 u
Number of boys in Group V
= 70 u - 14 u
= 56 u
Group U : Group V
54 + 56 : 6 + 14
110 : 20
(÷10)11 : 2
(b)
Number of boys in Group U = 14 u
Since the number of boys in Group U is 14 u, it must be multiple of 14.
Number of sets of 14
= 30 ÷ 14
= 2 r 2
Since the number of boys in Group U is more than 30, the number of sets must be 1 more than 2.
1 u = 2 + 1 = 3
Smallest possible number of students
= 60 u + 70 u
= 130 u
= 130 x 3
= 390
Answer(s): (a) 11 : 2; (b) 390