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 40% of the boys are in Group A. The rest of the pupils are in Group B.
- What is the ratio of the number of pupils in Group B to Group A? Give your answer in the simplest form.
- The number of boys in Group A is more than 60. What is the smallest possible total number of pupils taking part in the quiz?
Girls |
Boys |
10 u |
40 u |
Group A |
Group B |
Group A |
Group B |
2 u |
8 u |
16 u |
24 u |
(a)
Girls : Boys
1 : 4
10 : 40
Number of girls in Group A
= 20% x 10 u
=
20100 x 10 u
= 2 u
Number of girls in Group B
= 10 u - 2 u
= 8 u
Number of boys in Group A
= 40% x 40 u
=
40100 x 40 u
= 16 u
Number of boys in Group B
= 40 u - 16 u
= 24 u
Group A : Group B
8 + 24 : 2 + 16
32 : 18
(÷2)16 : 9
(b)
Number of boys in Group A = 16 u
Since the number of boys in Group A is 16 u, it must be multiple of 16.
Number of sets of 16
= 60 ÷ 16
= 3 r 12
Since the number of boys in Group A is more than 60, the number of sets must be 1 more than 3.
1 u = 3 + 1 = 4
Smallest possible number of pupils
= 10 u + 40 u
= 50 u
= 50 x 4
= 200
Answer(s): (a) 16 : 9; (b) 200