PSLE The number of girls and boys taking part in a quiz are in the ratio 1 : 4. These pupils are put into two groups. 20% of the girls and 10% 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 30. What is the largest possible total number of pupils taking part in the quiz?
Girls |
Boys |
10 u |
40 u |
Group E |
Group F |
Group E |
Group F |
2 u |
8 u |
4 u |
36 u |
(a)
Girls : Boys
1 : 4
10 : 40
Number of girls in Group E
= 20% x 10 u
=
20100 x 10 u
= 2 u
Number of girls in Group F
= 10 u - 2 u
= 8 u
Number of boys in Group E
= 10% x 40 u
=
10100 x 40 u
= 4 u
Number of boys in Group F
= 40 u - 4 u
= 36 u
Group F : Group E
8 + 36 : 2 + 4
44 : 6
(÷2)22 : 3
(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
= 30 ÷ 8
= 3 r 6
Since the number of girls in Group F is less than 30, the number of sets must be 3.
1 u = 3
Largest possible number of pupils
= 10 u + 40 u
= 50 u
= 50 x 3
= 150
Answer(s): (a) 22 : 3; (b) 150