PSLE The number of boys and girls taking part in a contest are in the ratio 3 : 8. These pupils are put into two groups. 60% of the boys and 20% of the girls 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 B is fewer than 70. What is the largest possible total number of pupils taking part in the contest?
Boys |
Girls |
30 u |
80 u |
Group A |
Group B |
Group A |
Group B |
18 u |
12 u |
16 u |
64 u |
(a)
Boys : Girls
3 : 8
30 : 80
Number of boys in Group A
= 60% x 30 u
=
60100 x 30 u
= 18 u
Number of boys in Group B
= 30 u - 18 u
= 12 u
Number of girls in Group A
= 20% x 80 u
=
20100 x 80 u
= 16 u
Number of girls in Group B
= 80 u - 16 u
= 64 u
Group B : Group A
12 + 64 : 18 + 16
76 : 34
(÷2)38 : 17
(b)
Number of boys in Group B = 12 u
Since the number of boys in Group B is 12 u, it must be multiple of 12.
Number of sets of 12
= 70 ÷ 12
= 5 r 10
Since the number of boys in Group B is less than 70, the number of sets must be 5.
1 u = 5
Largest possible number of pupils
= 30 u + 80 u
= 110 u
= 110 x 5
= 550
Answer(s): (a) 38 : 17; (b) 550