PSLE The number of boys and girls taking part in a contest are in the ratio 3 : 4. These pupils are put into two groups. 80% of the boys and 10% of the girls are in Group P. The rest of the pupils are in Group Q.
- What is the ratio of the number of pupils in Group Q to Group P? Give your answer in the simplest form.
- The number of boys in Group Q is fewer than 40. What is the largest possible total number of pupils taking part in the contest?
Boys |
Girls |
30 u |
40 u |
Group P |
Group Q |
Group P |
Group Q |
24 u |
6 u |
4 u |
36 u |
(a)
Boys : Girls
3 : 4
30 : 40
Number of boys in Group P
= 80% x 30 u
=
80100 x 30 u
= 24 u
Number of boys in Group Q
= 30 u - 24 u
= 6 u
Number of girls in Group P
= 10% x 40 u
=
10100 x 40 u
= 4 u
Number of girls in Group Q
= 40 u - 4 u
= 36 u
Group Q : Group P
6 + 36 : 24 + 4
42 : 28
(÷14)3 : 2
(b)
Number of boys in Group Q = 6 u
Since the number of boys in Group Q is 6 u, it must be multiple of 6.
Number of sets of 6
= 40 ÷ 6
= 6 r 4
Since the number of boys in Group Q is less than 40, the number of sets must be 6.
1 u = 6
Largest possible number of pupils
= 30 u + 40 u
= 70 u
= 70 x 6
= 420
Answer(s): (a) 3 : 2; (b) 420