PSLE The number of boys and girls taking part in a test are in the ratio 3 : 5. These pupils are put into two groups. 50% of the boys and 30% of the girls are in Group Q. The rest of the pupils are in Group R.
- What is the ratio of the number of pupils in Group R to Group Q? Give your answer in the simplest form.
- The number of boys in Group R is fewer than 40. What is the largest possible total number of pupils taking part in the test?
Boys |
Girls |
30 u |
50 u |
Group Q |
Group R |
Group Q |
Group R |
15 u |
15 u |
15 u |
35 u |
(a)
Boys : Girls
3 : 5
30 : 50
Number of boys in Group Q
= 50% x 30 u
=
50100 x 30 u
= 15 u
Number of boys in Group R
= 30 u - 15 u
= 15 u
Number of girls in Group Q
= 30% x 50 u
=
30100 x 50 u
= 15 u
Number of girls in Group R
= 50 u - 15 u
= 35 u
Group R : Group Q
15 + 35 : 15 + 15
50 : 30
(÷10)5 : 3
(b)
Number of boys in Group R = 15 u
Since the number of boys in Group R is 15 u, it must be multiple of 15.
Number of sets of 15
= 40 ÷ 15
= 2 r 10
Since the number of boys in Group R is less than 40, the number of sets must be 2.
1 u = 2
Largest possible number of pupils
= 30 u + 50 u
= 80 u
= 80 x 2
= 160
Answer(s): (a) 5 : 3; (b) 160