PSLE The number of girls and boys taking part in a contest are in the ratio 5 : 4. These pupils are put into two groups. 50% of the girls and 20% 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 80. What is the largest possible total number of pupils taking part in the contest?
Girls |
Boys |
50 u |
40 u |
Group U |
Group V |
Group U |
Group V |
25 u |
25 u |
8 u |
32 u |
(a)
Girls : Boys
5 : 4
50 : 40
Number of girls in Group U
= 50% x 50 u
=
50100 x 50 u
= 25 u
Number of girls in Group V
= 50 u - 25 u
= 25 u
Number of boys in Group U
= 20% x 40 u
=
20100 x 40 u
= 8 u
Number of boys in Group V
= 40 u - 8 u
= 32 u
Group V : Group U
25 + 32 : 25 + 8
57 : 33
(÷3)19 : 11
(b)
Number of girls in Group V = 25 u
Since the number of girls in Group V is 25 u, it must be multiple of 25.
Number of sets of 25
= 80 ÷ 25
= 3 r 5
Since the number of girls in Group V is less than 80, the number of sets must be 3.
1 u = 3
Largest possible number of pupils
= 50 u + 40 u
= 90 u
= 90 x 3
= 270
Answer(s): (a) 19 : 11; (b) 270