PSLE The number of girls and boys taking part in a contest are in the ratio 1 : 5. These pupils are put into two groups. 10% of the girls and 30% of the boys are in Group U. The rest of the pupils are in Group V.
- What is the ratio of the number of pupils in Group V to Group U? Give your answer in the simplest form.
- The number of girls in Group V is fewer than 60. What is the largest possible total number of pupils taking part in the contest?
Girls |
Boys |
10 u |
50 u |
Group U |
Group V |
Group U |
Group V |
1 u |
9 u |
15 u |
35 u |
(a)
Girls : Boys
1 : 5
10 : 50
Number of girls in Group U
= 10% x 10 u
=
10100 x 10 u
= 1 u
Number of girls in Group V
= 10 u - 1 u
= 9 u
Number of boys in Group U
= 30% x 50 u
=
30100 x 50 u
= 15 u
Number of boys in Group V
= 50 u - 15 u
= 35 u
Group V : Group U
9 + 35 : 1 + 15
44 : 16
(÷4)11 : 4
(b)
Number of girls in Group V = 9 u
Since the number of girls in Group V is 9 u, it must be multiple of 9.
Number of sets of 9
= 60 ÷ 9
= 6 r 6
Since the number of girls in Group V is less than 60, the number of sets must be 6.
1 u = 6
Largest possible number of pupils
= 10 u + 50 u
= 60 u
= 60 x 6
= 360
Answer(s): (a) 11 : 4; (b) 360