PSLE The number of girls and boys taking part in a contest are in the ratio 2 : 3. These pupils are put into two groups. 60% of the girls and 20% of the boys are in Group E. The rest of the pupils are in Group F.
- What is the ratio of the number of pupils in Group F to Group E? Give your answer in the simplest form.
- The number of girls in Group F is fewer than 50. What is the largest possible total number of pupils taking part in the contest?
Girls |
Boys |
20 u |
30 u |
Group E |
Group F |
Group E |
Group F |
12 u |
8 u |
6 u |
24 u |
(a)
Girls : Boys
2 : 3
20 : 30
Number of girls in Group E
= 60% x 20 u
=
60100 x 20 u
= 12 u
Number of girls in Group F
= 20 u - 12 u
= 8 u
Number of boys in Group E
= 20% x 30 u
=
20100 x 30 u
= 6 u
Number of boys in Group F
= 30 u - 6 u
= 24 u
Group F : Group E
8 + 24 : 12 + 6
32 : 18
(÷2)16 : 9
(b)
Number of girls in Group F = 8 u
Since the number of girls in Group F is 8 u, it must be multiple of 8.
Number of sets of 8
= 50 ÷ 8
= 6 r 2
Since the number of girls in Group F is less than 50, the number of sets must be 6.
1 u = 6
Largest possible number of pupils
= 20 u + 30 u
= 50 u
= 50 x 6
= 300
Answer(s): (a) 16 : 9; (b) 300